Set Topology

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Point Set Topology

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Author : Steven A. Gaal
language : en
Publisher: Courier Corporation
Release Date : 2009-04-23

Point Set Topology written by Steven A. Gaal and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-23 with Mathematics categories.

Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.

Elements Of Point Set Topology

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Author : John D. Baum
language : en
Publisher: Courier Corporation
Release Date : 1991-01-01

Elements Of Point Set Topology written by John D. Baum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Set Topology

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Author : R. Vaidyanathaswamy
language : en
Publisher: Courier Corporation
Release Date : 1960-01-01

Set Topology written by R. Vaidyanathaswamy and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960-01-01 with Mathematics categories.

This introductory text covers the algebra of subsets and of rings and fields of sets, complementation and ideal theory in the distributive lattice, closure function, neighborhood topology, much more. Includes numerous exercises. 1960 edition.

Point Set Topology

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Author : Rafael López
language : en
Publisher: Springer Nature
Release Date : 2024-05-31

Point Set Topology written by Rafael López and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-31 with Mathematics categories.

This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular. Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group. Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.

Topology

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Author : Donald W. Kahn
language : en
Publisher:
Release Date : 1975

Topology written by Donald W. Kahn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.

Advanced text includes elementary general topology, algebraic topology, 2-manifolds covering spaces and fundamental groups. Problems, with selected solutions.

Handbook Of Set Theoretic Topology

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Author : K. Kunen
language : en
Publisher: Elsevier
Release Date : 2014-06-28

Handbook Of Set Theoretic Topology written by K. Kunen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

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 without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Introduction To General Topology

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Author : K. D. Joshi
language : en
Publisher: New Age International
Release Date : 1983

Introduction To General Topology written by K. D. Joshi and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Topology categories.

Elementary Point Set Topology

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Author : Andre L. Yandl
language : en
Publisher: Courier Dover Publications
Release Date : 2016-05-18

Elementary Point Set Topology written by Andre L. Yandl and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-18 with Mathematics categories.

This versatile, original approach, which focuses on learning to read and write proofs, serves as both an introductory treatment and a bridge between elementary calculus and more advanced courses. 2016 edition.

A Course In Point Set Topology

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Author : John B. Conway
language : en
Publisher: Springer
Release Date : 2016-08-23

A Course In Point Set Topology written by John B. Conway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-23 with Mathematics categories.

This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.

General Topology

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Author : John L. Kelley
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-17

General Topology written by John L. Kelley and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-17 with Mathematics categories.

"The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure," noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive preliminary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, the Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. The book concludes with an extensive index that provides supplementary material on elementary set theory.