Introduction To Set Theory And Topology

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Introduction to Set Theory and Topology

Author : Kazimierz Kuratowski
Publisher : Elsevier
ISBN 13 : 1483151638
Total Pages : 352 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Introduction to Set Theory and Topology by : Kazimierz Kuratowski

Download or read book Introduction to Set Theory and Topology written by Kazimierz Kuratowski and published by Elsevier. This book was released on 2014-07-10 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Elementary Concepts of Topology

Author : Paul Alexandroff
Publisher : Courier Corporation
ISBN 13 : 0486155064
Total Pages : 68 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff

Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Handbook of Set-Theoretic Topology

Author : K. Kunen
Publisher : Elsevier
ISBN 13 : 148329515X
Total Pages : 1282 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Handbook of Set-Theoretic Topology by : K. Kunen

Download or read book Handbook of Set-Theoretic Topology written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Point Set Topology

Author : John D. Baum
Publisher : Courier Corporation
ISBN 13 : 0486668266
Total Pages : 164 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Elements of Point Set Topology by : John D. Baum

Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Combinatorial Introduction to Topology

Author : Michael Henle
Publisher : Courier Corporation
ISBN 13 : 9780486679662
Total Pages : 340 pages
Book Rating : 4.6/5 (796 download)

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Book Synopsis A Combinatorial Introduction to Topology by : Michael Henle

Download or read book A Combinatorial Introduction to Topology written by Michael Henle and published by Courier Corporation. This book was released on 1994-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Introduction to Topology

Author : Bert Mendelson
Publisher : Courier Corporation
ISBN 13 : 0486135098
Total Pages : 226 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Topology by : Bert Mendelson

Download or read book Introduction to Topology written by Bert Mendelson and published by Courier Corporation. This book was released on 2012-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Philosophical Introduction to Set Theory

Author : Stephen Pollard
Publisher : Courier Dover Publications
ISBN 13 : 0486797147
Total Pages : 196 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Philosophical Introduction to Set Theory by : Stephen Pollard

Download or read book Philosophical Introduction to Set Theory written by Stephen Pollard and published by Courier Dover Publications. This book was released on 2015-07-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Introduction to Topology

Author : Crump W. Baker
Publisher :
ISBN 13 : 9781575240084
Total Pages : 155 pages
Book Rating : 4.2/5 (4 download)

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Book Synopsis Introduction to Topology by : Crump W. Baker

Download or read book Introduction to Topology written by Crump W. Baker and published by . This book was released on 1997 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental concepts of general topology are covered in this text whic can be used by students with only an elementary background in calculus. Chapters cover: sets; functions; topological spaces; subspaces; and homeomorphisms.

Point Set Topology

Author : Steven A. Gaal
Publisher : Courier Corporation
ISBN 13 : 0486472221
Total Pages : 338 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Point Set Topology by : Steven A. Gaal

Download or read book Point Set Topology written by Steven A. Gaal and published by Courier Corporation. This book was released on 2009-04-23 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Set Theory for Beginners

Author : Steve Warner
Publisher :
ISBN 13 : 9780999811764
Total Pages : pages
Book Rating : 4.8/5 (117 download)

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Book Synopsis Set Theory for Beginners by : Steve Warner

Download or read book Set Theory for Beginners written by Steve Warner and published by . This book was released on 2019-02-18 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Set Theory for BeginnersSet Theory for Beginners consists of a series of basic to intermediate lessons in set theory. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Set Theory for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in set theory high school teachers working with advanced math students students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and mathematical logic. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Set Theory Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets Lesson 2 - Subsets Lesson 3 - Operations on Sets Lesson 4 - Relations Lesson 5 - Equivalence Relations and Partitions Lesson 6 - Functions Lesson 7 - Equinumerosity Lesson 8 - Induction and Recursion on N Lesson 9 - Propositional Logic Lesson 10 - First-order Logic Lesson 11 - Axiomatic Set Theory Lesson 12 - Ordinals Lesson 13 - Cardinals Lesson 14 - Martin's Axiom Lesson 15 - The Field of Real Numbers Lesson 16 - Clubs and Stationary Sets

Introduction to Topology

Author : Theodore W. Gamelin
Publisher : Courier Corporation
ISBN 13 : 0486320189
Total Pages : 258 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Introduction to Topology by : Theodore W. Gamelin

Download or read book Introduction to Topology written by Theodore W. Gamelin and published by Courier Corporation. This book was released on 2013-04-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Topology for Beginners

Author : Steve Warner
Publisher :
ISBN 13 : 9780999811771
Total Pages : 282 pages
Book Rating : 4.8/5 (117 download)

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Book Synopsis Topology for Beginners by : Steve Warner

Download or read book Topology for Beginners written by Steve Warner and published by . This book was released on 2019-04-25 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology for Beginners consists of a series of basic to intermediate lessons in topology. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Topology for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in topology. high school teachers working with advanced math students. students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and topology. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Topology Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets and Subsets Lesson 2 - Operations on Sets Lesson 3 - Relations Lesson 4 - Functions and Equinumerosity Lesson 5 - Number Systems and Induction Lesson 6 - Algebraic Structures and Completeness Lesson 7 - Basic Topology of R and C Lesson 8 - Continuity in R and C Lesson 9 - Topological Spaces Lesson 10 - Separation and Countability Lesson 11 - Metrizable Spaces Lesson 12 - Compactness Lesson 13 - Continuity and Homeomorphisms Lesson 14 - Connectedness Lesson 15 - Function Spaces Lesson 16 - Algebraic Topology

Topology

Author : Tai-Danae Bradley
Publisher : MIT Press
ISBN 13 : 0262359626
Total Pages : 167 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Topology by : Tai-Danae Bradley

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.

Introduction to Set Theory and Topology

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (637 download)

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Book Synopsis Introduction to Set Theory and Topology by :

Download or read book Introduction to Set Theory and Topology written by and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Essentials of Topology with Applications

Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1420089757
Total Pages : 422 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Essentials of Topology with Applications by : Steven G. Krantz

Download or read book Essentials of Topology with Applications written by Steven G. Krantz and published by CRC Press. This book was released on 2009-07-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings Readers Up to Speed in This Important and Rapidly Growing AreaSupported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological

A Book of Set Theory

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Set Theory by : Charles C Pinter

Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Homology Theory

Author : James W. Vick
Publisher : Springer Science & Business Media
ISBN 13 : 1461208815
Total Pages : 258 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Homology Theory by : James W. Vick

Download or read book Homology Theory written by James W. Vick and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.