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Topics In General Topology
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Book Synopsis Topics in General Topology by : K. Morita
Download or read book Topics in General Topology written by K. Morita and published by Elsevier. This book was released on 1989-08-04 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments. The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.
Book Synopsis General Topology by : John L. Kelley
Download or read book General Topology written by John L. Kelley and published by Courier Dover Publications. This book was released on 2017-03-07 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.
Book Synopsis Recent Progress in General Topology III by : K.P. Hart
Download or read book Recent Progress in General Topology III written by K.P. Hart and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 903 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Book Synopsis Modern General Topology by : Jun-Iti Nagata
Download or read book Modern General Topology written by Jun-Iti Nagata and published by Elsevier. This book was released on 2014-05-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and approaches employed in pure and applied mathematics, including spaces, cardinal and ordinal numbers, and mappings. The publication first elaborates on set, cardinal and ordinal numbers, basic concepts in topological spaces, and various topological spaces. Discussions focus on metric space, axioms of countability, compact space and paracompact space, normal space and fully normal space, subspace, product space, quotient space, and inverse limit space, convergence, mapping, and open basis and neighborhood basis. The book then ponders on compact spaces and related topics, as well as product of compact spaces, compactification, extensions of the concept of compactness, and compact space and the lattice of continuous functions. The manuscript tackles paracompact spaces and related topics, metrizable spaces and related topics, and topics related to mappings. Topics include metric space, paracompact space, and continuous mapping, theory of inverse limit space, theory of selection, mapping space, imbedding, metrizability, uniform space, countably paracompact space, and modifications of the concept of paracompactness. The book is a valuable source of data for mathematicians and researchers interested in modern general topology.
Download or read book General Topology written by J. Dixmier and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a real variable: uniform continuity, uniform convergence, equicontinuity, Bolzano-Weierstrass theorem (this work is historically inseparable from the attempts to define with precision what the real numbers are). Cauchy was one of the pioneers in this direction, but the errors that slip into his work prove how hard it was to isolate the right concepts. Cantor came along a bit later; his researches into trigonometric series led him to study in detail sets of points of R (whence the concepts of open set and closed set in R, which in his work are intermingled with much subtler concepts). The foregoing alone does not justify the very general framework in which this course is set. The fact is that the concepts mentioned above have shown themselves to be useful for objects other than the real numbers.
Book Synopsis Topics in General Topology by : Kiiti Morita
Download or read book Topics in General Topology written by Kiiti Morita and published by Elsevier. This book was released on 1989 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments. The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.
Book Synopsis Recent Progress in General Topology II by : M. Husek
Download or read book Recent Progress in General Topology II written by M. Husek and published by Elsevier. This book was released on 2002-11-13 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
Book Synopsis Recent Progress in General Topology II by : M. Husek
Download or read book Recent Progress in General Topology II written by M. Husek and published by Elsevier. This book was released on 2002-11-13 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. It follows freely the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as: R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
Book Synopsis Geometric Aspects of General Topology by : Katsuro Sakai
Download or read book Geometric Aspects of General Topology written by Katsuro Sakai and published by Springer Science & Business Media. This book was released on 2013-07-22 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.
Download or read book General Topology written by Tom Richmond and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-07-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 mathematics designed to model loss-of-resolution situations.
Book Synopsis The General Topology of Dynamical Systems by : Ethan Akin
Download or read book The General Topology of Dynamical Systems written by Ethan Akin and published by American Mathematical Soc.. This book was released on 1993 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.
Book Synopsis General Topology and Homotopy Theory by : I.M. James
Download or read book General Topology and Homotopy Theory written by I.M. James and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group theory. This book is based on a course of 16 graduate lectures given at Oxford and elsewhere from time to time. In a course of that length one cannot discuss too many topics without being unduly superficial. However, this was never intended as a treatise on the subject but rather as a short introductory course which will, I hope, prove useful to specialists and non-specialists alike. The introduction contains a description of the contents. No algebraic or differen tial topology is involved, although I have borne in mind the needs of students of those branches of the subject. Exercises for the reader are scattered throughout the text, while suggestions for further reading are contained in the lists of references at the end of each chapter. In most cases these lists include the main sources I have drawn on, but this is not the type of book where it is practicable to give a reference for everything.
Book Synopsis Principles of Topology by : Fred H. Croom
Download or read book Principles of Topology written by Fred H. Croom and published by Courier Dover Publications. This book was released on 2016-02-17 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.
Book Synopsis Point-set Topology With Topics: Basic General Topology For Graduate Studies by : Robert Andre
Download or read book Point-set Topology With Topics: Basic General Topology For Graduate Studies written by Robert Andre and published by World Scientific. This book was released on 2024-01-19 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook can be used as introduction to a general topology course at undergraduate and graduate level courses. However, many parts of this book present topological concepts that apply directly to functional analysis, which will be of interest to scholars working in those fields.In Part I, readers are eased into the main subject matter of general topology, being presented with summaries of normed vector spaces and metric spaces. Parts II to VI form the core material contained in most Basic General Topology courses. After having worked through the most fundamental concepts of topology, the reader will be exposed to brief introductions to more specialized or advanced topics of pointset topology. These are presented in Part VII in the form of a sequence of chapters, many of which can be read or studied independently or in short sequences of two or three chapters, provided that the student has mastered the previous sections.Chapters related to the more basic ideas of general topology are followed by a collection of 'concept review' questions, the answers to which are found in the main body of the text. These questions highlight the main concepts presented in that chapter, as well as ideas that are often overlooked when first encountered, which will help to test the students' understanding. The efforts required in answering correctly such questions will provide the student with the ability to solve more complex problems in the exercises collected at the end of each section.
Download or read book Topology written by Tai-Danae Bradley and published by MIT Press. This book was released on 2020-08-18 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Book Synopsis Open Problems in Topology II by : Elliott M. Pearl
Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world
Author :O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Publisher :American Mathematical Soc. ISBN 13 :9780821886250 Total Pages :432 pages Book Rating :4.8/5 (862 download)
Book Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Download or read book Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and published by American Mathematical Soc.. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
