Общая топология

М.: МЦНМО, 1995. — 111 с. — ISBN-13 5-900916-04-9. Книга представляет собой вводный курс топологии. Основные понятия сначала описываются на интуитивно понятном уровне, а затем постепенно уточняются и становятся вполне строгими. Это позволяет сразу же заняться содержательными топологическими задачами. Книга снабжена многочисленными иллюстрациями, которые нередко более важны для...

Изд. 3-е. испр. и доп. — М.: Ленанд, 2015. — 448 с. — (Классический учебник МГУ.) В пособии содержатся первые понятия топологии, общая топология, теория гомотопий, даётся классификация двумерных поверхностей, рассматриваются основы теории гладких многообразий и расслоений, элементы теории Морса, излагаются теории симплициальных, сингулярных и клеточных гомологий с приложениями...

3-е изд. — М.: МЦНМО, 2012. — 112 с. — ISBN: 978-5-94057-903-8 (интерактивное оглавление) Книга представляет собой вводный курс топологии. Основные понятия сначала описываются на интуитивно понятном уровне, а затем постепенно уточняются и становятся вполне строгими. Это позволяет сразу же заняться содержательными топологическими задачами. Книга снабжена многочисленными...

М., Наука, 1968 г. – 384 с. Монография посвящена общей, или теоретико-множественной, топологии. В ней собраны наиболее важные результаты из этой области математики. Большое внимание в книге уделено таким фундаментальным вопросам, как сходимость по направленному множеству, топологические произведения и фактор-пространства, метризационные теоремы, теория бикомпактных пространств,...

2nd ed. — Pearson Education Limited, 2014. — 560 р. For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This text is designed to provide instructors with a convenient single text resource for bridging between...

2nd Edition. — Springer, 2011. — xxv, 360 p. — (Undergraduate Texts in Mathematics Series). — ISBN 978-1-4419-7126-5, 978-1-4419-7127-2. Proofs and Fundamentals: A First Course in Abstract Mathematics 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets,...

Москва: Мир, 1986. — 752 с. Энциклопедически полное и сбалансированное изложение обширного круга вопросов по общей топологии, написанное известным польским математиком. Книга может использоваться в качестве справочника и как вводное учебное пособие по общей топологии. Для математиков разных специальностей, для всех изучающих и использующих методы общей топологии. Разделы:...

М.: Издательство ЦПИ при механико- математическом факультете МГУ.— 138 с. Метрические пространства. Канторово совершенное множество. Непрерывные отображения метрических пространств. Кривая Пеано. Топологические пространства. Непрерывные отображения топологических пространств. Аксиомы отделимости. Лемма Урысона. Разбиение единицы. Теорема Брауэра- Титце- Урысона о...

Геометрия отображений отрезков, кривых, окружностей и кругов. — М.: Мир, 1967. — 224с. — (Современная математика) — перевод с английского И.А. Ванштейна. Книга посвящена основным и простейшим понятиям топологии. На примере двух важных теорем авторы показывают, как эти понятия возникают, как они позволяют правильно понять и точно сформулировать некоторые утверждения и как с...

Second Edition. — Prentice Hall, 2000. — 537 p. This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate...

М.: МГУ, 1989.—222 с. В монографии систематически излагается топологическая C p -теория — активно развивающаяся область современной математики. Топологические свойства пространства C p (X) и его подпространств представляют большой интерес для общей топологии, топологической алгебры и функционального анализа. Монография содержит много оригинальных результатов новейших...

СПб.: Лань, 2010. — 368 с. Книга является введением в современные разделы общей топологии. Первые три главы представляют собой изложение фактов теории множеств с так называемой «наивной» точки зрения. В главах 4–6 дается изложение основных топологических фактов, касающихся метрических и топологических пространств. Особое внимание при этом обращается на метризационные теоремы и...

Pearson Prentice Hall. 2008. - 507p. - ISBN: 978-81-317-2692-1, English. Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in...

М.: Мир, 1966. — 594 с. пер. с англ., Русский. Монография известного ученого, вице-президента Академии наук Польской Народной Республики, иностранного члена АН СССР Казимира Куратовского - выдающееся явление в математической литературе. Она представляет собой наиболее полное и легко читаемое сочинение, охватывающее большинство разделов современной общей топологии. Монография...

Москва: Государственное издательство технико-теоретической литературы, 1954. — 142 с. Предлагаемая книга посвящена разъяснению одного из самых основных понятий математики — понятия линии. Кажущееся на первый взгляд очень простым, понятие линии требует для своего общего и полного определения довольно значительных сведений из теории точечных множеств, получившей особенное...

Springer International Publishing, Switzerland, 2015. — 315 p. — (UNITEXT 91) — ISBN: 3319169572 This textbook offers a primer in general topology (point-set topology), together with an introduction to algebraic topology. It is meant primarily for students with a mathematical background that is usually taught in the first year of undergraduate degrees in Mathematics and...

Springer, 2010. — 234 pages. Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and...

2nd Edition. — Prentice Hall, 2000. — 537 p. — ISBN: 0131816292. This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic...

McGraw-Hill, 1965. — 239 p. Master topology with Schaum's-the high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Outlines because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study...

Springer, 2019. — 458 p. — ISBN: 9811369534. Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas...

Пер. с франц. С.Н. Крачковского. Под ред. Д.А. Райкова. — М.: Наука, 1968. — 275 с.: ил. Наряду с алгебраическими структурами (группами, кольцами, телами и т. д. ), которые составляли предмет второй книги этого сочинения, во всех разделах анализа встречаются структуры другого рода: структуры, в которых придается математический смысл интуитивным понятиям предела, непрерывности и...

Метрические пространства Топологические пространства Замкнутые множества Аксиомы отделимости Компакты Свойства компактов Поверхности Различность модельных поверхностей

М.: Наука, Главная редакция физико-математической литературы, 1977. — 368 c. Первые три главы книги представляют собой изложение фактов теории множеств с так называемой «наивной» точки зрения. В главах 4—6 даётся изложение основных топологических фактов, касающихся метрических и топологических пространств. Особое внимание при этом обращается на метризационные теоремы и понятия...

2-е изд., стереотип. — М.: МЦНМО, 2014. — 38 с. — ISBN: 978-5-4439-3009-1. В этой брошюре содержатся задачи к трехсеместровому курсу топологии, который неоднократно читался для студентов первого и второго курса НМУ (Независимый Московский Университет). В первом семестре обсуждаются топологические пространства, фундаментальная группа и накрытия, во втором семестре —...

World Scientific, 2014. — 261 p. — ISBN: 9814583812, 9789814583817 The present book offers a good introduction to basic general topology throughout solved exercises and one of the main aims is to make the understanding of topology an easy task to students by proposing many different and interesting exercises with very detailed solutions, something that it is not easy to find in...

Данный курс лекций издан для студентов физико-математического факультета Елецкого государственного университета им. И. А. Бунина. Содержание. Топологические пространства. Окрестность точки, база топологии, замкнутые множества. Топологические подпространства. Непрерывность отображений топологических пространств. Гомеоморфизмы топологических пространств. Предмет топологии....

Springer, 2014. — 136 p. — ISBN: 3319096796, 9783319096797 This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need...

Учебное пособие, 2-е изд. испр. и доп. — М.: Физматлит, 2006. — 332 с. — ISBN: 5-9221-0618-Х. В учебном пособии, представляющем собой изложение курса лекций, читаемых авторами на механико-математическом факультете МГУ, рассмотрены основные понятия теории топологических пространств: спектры, произведения и степени топологических пространств, пространства замкнутых и бикомпактных...

D. Van Nostrand Company, Ltd., 1955. — 298 p. This book is a systematic exposition of the part of general topology which has proven useful in several branches of mathematics. It is especially intended as background for modern analysis, and I have, with difficulty, been prevented by my friends from labeling it: What Every Young Analyst Should Know. The book, which is based on...

Учеб. пособие для вузов. — М.: Высшая школа, 1979. — 336 с.: ил. Книга содержит современное изложение понятий, результатов и методов общей топологии. Весь материал разбит на три раздела. В первом из них строятся изучаемые объекты (топологические пространства) и морфизмы (их непрерывные отображении) и, кроме того, особое внимание уделено топологическим и изотопическим...

Addison-Wesley Publishing Co., 1961. — 374 p. We have designed this book as a text for a one-year first course in topology. A few words about prerequisites for a successful study of this book are in order. It has been our experience that the student should have had the elements of set theory and should have had, or be studying concurrently, courses in group theory and the...

AMS, 2008. — 400 pages. This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from...

New York: Springer, 2022. — 523 p. This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that...

2nd Edition. — World Scientific Publishing, 2017. — 375 p. — ISBN: 9789813146938. "With the publication of the second edition, the author has made a good book even better. The author's writing style is clear and detailed, and therefore this book should be accessible to most reasonably well-prepared college students. The exercises come in a variety of forms. Most exercises have...

Springer, 2022. — 488 p. — ISBN 978-981-16-6549-3. This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy...

Sydney: 2017. — 645 p. This book provides a thorough grounding in general topology. There are many exercises in this book. Only by working through a good number of exercises will you master this course. I have not provided answers to the exercises, and I have no intention of doing so. It is my opinion that there are enough worked examples and proofs within the text itself, that...

Elsevier Science, 2004. - 536 pages. ISBN: 0444503552 General Topology has experienced rapid growth during the past fifty years, and nowadays its language and concepts pervade much of modern day mathematics. This book is intended for a broad community of scholars and students working in mathematics and other areas who want to become acquainted quickly with the terminology and...

Sydney: 2019. — 767 p. This book provides a thorough grounding in general topology . There are many exercises in this book. Only by working through a good number of exercises will you master this course. I have not provided answers to the exercises, and I have no intention of doing so. It is my opinion that there are enough worked examples and proofs within the text itself,...

Учебное пособие. — СПб.: Университет ИТМО, 2019. — 51 с. Пособие представляет собой конспект лекций, содержащих введение в общую топологию, теорию дифференцируемых многообразий, а также элементы алгебраической топологии. Данное введение служит основой для курсов по дифференциальной геометрии, математической физике, а также теории поля. Пособие содержит шесть лекций,...

Berlin/Boston: Germany: Higher Education Press, Walter de Gruyter GmbH, De Gruyter Graduate, 2016. — 250 p. — ISBN: 978-3-11-037815-3. For mathematicians, topology is a fundamental mathematical language widely used in many fields. For students, topology is an intellectually challenging and rewarding subject. This textbook aims to address the subject of topology from both...

Mathematical Association of America, 2001. — 169 p. The authors of First Concepts of Topology demonstrate the power, the flavor and the adaptability of topology, one of the youngest branches of mathematics, in proving so-called existence theorems. An existence theorem asserts that a solution to some given problem exists; thus it assures those who hunt for a solution that their...

Cengage Learning Asia, 2002. - 324 pages. This text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological...

Birkhäuser, 2012. - 495 pages. The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional...

М.: МЦНМО, 2008. — 40 с. — ISBN: 978-5-94057-349-4. В этой брошюре содержатся задачи к трехсеместровому курсу топологии, который неоднократно читался для студентов первого и второго курса НМУ (Независимый Московский Университет). В первом семестре обсуждаются топологические пространства, фундаментальная группа и накрытия, во втором семестре — CW-комплексы, многообразия,...

Springer, 2022. — 384 p. — ISBN 9811665761. This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this...

Dordrecht: Springer Science+Business Media, 1997. — 381 p. — ISBN: 0792344790 This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology,...

Hong Kong University of Science and Technology, 2010. - 235 pages. Set and Map. Metric Space. Graph and Network. Topology. Basic Topological Concepts. Complex. Topological Properties. Surface. Topics in Point Set Topology.

Москва: Наука, 1974. — 424 с. Книга вводит читателя в область основных понятий и методов общей топологии своеобразным путем, а именно посредством задач, которые предлагаются читателю в порядке возрастающей трудности (на большинство задач предлагаются краткие описания решения). Никакой специальной подготовки книга не требует — она доступна студентам-математикам, начиная со...

Dover, 1974. — 186 pages. This introduction to topology eases readers into the subject by building a bridge from the familiar concepts of geometry to the formalized study of topology. Focuses on congruence classes defined by transformations in real Euclidean space, continuity, sets, functions, metric spaces, and topological spaces, and more. Exercises and Problems. Includes 101...

Atlantis Press, 2014. - 898 pages. ISBN: 978-9462390232 The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held...

Учеб. -метод. пособие/сост. В. А. Долженков, Е. Г. Соловьева, И. В. Горчинский. Курск: Курск. гос. ун-т, 2006. – 63 с., eBook. Данное учебно-методическое пособие предназначено для студен-тов 1-го курса специальности 351500 «Математическое обеспечение и администрирование информационных систем» по курсу «Геометрия и топология» (количество часов 400). Пособие содержит...

Cambridge University Press, 2018. — 288 p. — (London Mathematical Society Student Texts 90). — ISBN: 978-1-107-10136-4 The notion of an (∞, 1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This...

Allyn & Bacon, 1966. — 460 p. In this book, my aim is to provide the reader with a foundation in general topology that will adequately prepare him for further work in a broad variety of mathematical disciplines. The arrangement of the material is such that the book can also serve as a reference for the more advanced mathematician. The reader is assumed to have a background of...

Lambert Academic Publishing, 2018. — 312 p. — ISBN: 6202199288. We have carefully wrote this book for those interested in concepts of topology for different branches of Mathematics that are used in a variety of applications in other scientific fields. What distinguishes this book from others is that it contains a very simple proofs and many new examples. This book introduces...

2nd Revised edition. — North Holland, 1985. — 522 p. This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first...

Springer Science+Business Media, 1998. — 419 p. — (History of Topology Volume 2). — ISBN: 978-90-481-5704-4. This account of the History of General Topology has grown out of the special session on this topic in San-Antonio, Texas, 1993. It was there that the idea grew to publish a book on the historical development of General Topology. Moreover it was felt that it was important...

Springer Science+Business Media, 2001. — 418 p. — (History of Topology Volume 3). — ISBN: 978-90-481-5704-4. This volume mainly focuses on various comprehensive topological theories, with the exception of a paper on combinatorial topology versus point-set topology by I.M. James and a paper on the history of the normal Moore space problem by P. Nyikos. The history of the...

Sidney: Independently published, 2024. - 729 p. A recent addition to the Topology Without Tears book is Appendix 5 which contains the material for a first graduate course on topological groups . In particular, it contains the beautiful Pontryagin-van Kampen Duality Theorem for locally compact abelian groups and a description of the structure of locally compact abelian groups. I...

Topology Atlas, 2003. - 222 pages. This book consists of material originally appearing in the Problem Section of the journal Topology Proceedings since 1976 as well as some other well-known problem lists in general topology from the 1970's that have some connection to the journal. The problems have been updated with current information on solutions with bibliographic...

New York: Springer, 2007. — 186 p. — (Universitext). This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second...

2-е изд., доп. — М.: Наука. Физматлит, 1995. — 416 с. Содержит материал, составляющий основу топологических знаний. Излагаются понятия и теоремы общей и гомотопической топологии, дается классификация двумерных поверхностей, основные понятия гладких многообразий и их отображений, рассматриваются элементы теории Морса и теории гомологий с приложениями к неподвижным точкам.

М.: Московский государственный педагогический институт (МГПИ) имени В.И. Ленина, 1984. — 124 с. Общая топология Введение Гомеоморфные и негомеоморфные фигуры Аксиоматика П.С.Александрова топологического пространства Модели топологического пространства Непрерывность, гомеоморфизм, окрестность База топологического пространства, топологическое подпространств, произведение двух...

Dover Publications, 1961. — 57 pages. ISBN: 048660747X Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.

De Gruyter, 2020. — 319 p. The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and...

Marcel Dekker, 1990. - 287 pages. ISBN: 0824783492 Proceedings of the Northeast Conference on the subject at Wesleyan University, Connecticut, in June 1988. The two dozen papers, by mathematicians from the US, Canada, and the Netherlands, report on recent advances in topology for research mathematicians and graduate students.

М.: Физматлит, 2009. — 148 с. — ISBN: 978-5-9221-1038-9. Монография, оригинал которой был опубликован в 1929 г. на французском языке, посвящена основам общей топологии. Она является одним из первых систематических изложений теории компактных топологических пространств. Данную монографию можно рассматривать как один из вариантов «первой книги для чтения» по общей топологии. Она...

North-Holland, Elsevier B.V, 1984. — viii, 1274 p. — ISBN 978-0-444-86580-9, 0-444-86580-2, 0-444-70431-0, 978-0-444-70431-3. This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible...

2nd ed. — Springer, 2023. — 382 p. — (Unitext, 153). — ISBN 3031321413. This is an introductory textbook on general and algebraic topology , aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include : set theory and cardinal arithmetic; axiom of choice and Zorn's lemma;...

New York: Dover Publications, 2004. — 381 p. Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform...

М.: Наука, 1971. — 144 с. Эта монография представляет собою третье русское издание работы, оригинал которой был опубликован под заглавием Mémoire sur les espaces topologiques compacts, dédié à M. D. Egoroff par P. Alexandroff et P. Urysohn (Verhandelingen der Kon. Akademie van Weten-schappen te Amsterdam, Afdeeling Naturkunde, eerste sectie, deel XIV, 1929, стр. VIII + 96). Она...

Kluwer Academic Publishers, Springer Science + Business Media, Inc., 2004. — 333 p. — (Mathematics and Its Applications 571) — ISBN: 1402019637. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control Theory, Calculus of Variations, Probability Theory) are...

Springer, 2019. - 261 p. - (Atlantis Studies in Mathematics, 7). - ISBN: 3030222314. This book covers the fundamental results of the dimension theory of metrizable spaces , especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures...

New York: Springer, 2010. — 150 p. This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer­ sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions...

Sidney Morris, 2011. — 373 pages. This book provides a thorough grounding in general topology. From the table of contents: introduction, topological spaces, the Euclidian topology, limit points, homeomorphisms, continuous mappings, metric spaces, compactness, finite products, countable products, Tychonoff's theorem.

СПб.: ПОМИ, 1997 - 229 c. Эта книга является многолетней работой автора по битопологическим пространствам, и по-своему объему и содержанию является монографией, посвященной теории битопологических пространств и ее приложениям. Писалась она при поддержке Российского Фонда фундаментальных исследований (гранты 1994–1995 годов). Эта книга далеко не исчерпывает все, что относится к...

Amsterdam; New York: North-Holland Publishing Company; Warsaw: Polish Scientific Publishers, 1978. — x + 314 p. Dimension theory... gives the background in separable metric spaces in a reasonable way and exposes the student to enough of the theory for nonmetrizable spaces for him to learn to keep his wits about him when facing problems in this difficult area. One can use the...

De Gruyter, 2025. — 247 p. — (De Gruyter Textbook). This book is dedicated to metric spaces and their topology. The book starts with ZFC axioms. The real number system is constructed by both the Dedekind cut and the Cauchy sequence approach. The various examples and properties of metric spaces and normed linear spaces are discussed. The different distances between the sets are...

New York: Dover Publications, 2009. — 312 p. General topology offers a valuable tool to students of mathematics, particularly in courses involving complex, real, and functional analysis. This introductory treatment is essentially self-contained, and it features explanations and proofs that relate to every practical aspect of point-set topology. It will prove valuable to...

Hindustan Book Agency, 2011. — 117 p. Topological Preliminaries. The Haar measure on a locally compact group. Hilbert spaces and the spectral theorem. Compact groups and their representations.

Princeton, Princeton University Press, 1948, 184p. 1) Introduction 2) Dimension 0 3) Dimension n 4) Dimension of Euclidean Spaces 5) Covering and Imbedding Theorems 6) Mappings in Spheres and Applications 7) Dimension and Measure 8) Homology and Dimension Appendix: Non Separable Metric Spaces

Cambridge University Press, 1975. — 442 p. This book is concerned with the dimension theory of general topological spaces. It provides a complete and self-contained account of the theory laying particular emphasis on the dimensional properties of non-metrizable spaces. It is intended to serve as a reference work for mathematicians with an interest in general topology. It is...

American Mathematical Society, 2001. - 149 Pages. This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations,...

World Scientific Publishing, 2021. — 153 p. — ISBN 9811227417. This book is intended as a one-semester course in general topology, a.k.a. point-set topology, for undergraduate students as well as first-year graduate students. Such a course is considered a prerequisite for further studying analysis, geometry, manifolds, and certainly, for a career of mathematical research....

New York: Springer, 2018. — 451 p. This book is a significant companion text to the existing literature on continuum theory. It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. In this new edition...

American Mathematical Society, 2006. - 141 pages. ISBN: 0821838849 How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincaré argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to...

Sidney Morris, 2007. — 353 p. This book provides a thorough grounding in general topology. From the table of contents: introduction, topological spaces, the Euclidian topology, limit points, homeomorphisms, continuous mappings, metric spaces, compactness, finite products, countable products, Tychonoff's theorem.

AMS, 2008. — 261 p. General Topology Continuity Topological Properties Topological Constructions Topological Algebra Elements of Algebraic Topology Fundamental Group Covering Spaces and Calculation of Fundamental Groups Fundamental Group and Maps Cellular Techniques

Dissertation PhD. — Madison: University of Wisconsin–Madison, 2009. — 174 p. We present several results related to van Douwen’s Problem, which asks whether there is homogeneous compactum with cellularity exceeding c, the cardinality of the reals. For example, just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of...

Springer, 1998. — xvi, 261 p. — (Graduate Texts in Mathematics, 180). — ISBN 0-378-98412-7, 978-0-387-22767-2. A Course on Borel sets provides a thorough introduction to Borel sets and measurable selections and acts as a stepping stone to descriptive set theory by presenting important techniques such as universal sets, prewellordering, scales, etc. It is well suited for...

Lambert Academic Publishing, 2018. — 160 с. — ISBN: 978-613-9-81561-6. Цей посібник призначений для студентів та викладачів IV-V курсів вищих навчальних закладів фізико-математичного спрямування. Вивчення студентами різноманітноті інверсних відображень як різвовиду комформних відображень площини в рамках однойменного спецкурсу найкращим чином сприятиме узагальненню та зміцненню...