Verfügbarkeit: A Guide to Topology /

A Guide to Topology /:

A Guide to Topology is an introduction to basic topology. It covers point-set topology as well as Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, an...

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Bibliographische Detailangaben
1. Verfasser:	Krantz, Steven G. (Steven George), 1951-
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge : Cambridge University Press, 2012.
Schriftenreihe:	Dolciani mathematical expositions.
Schlagworte:	Topology. Topologie. MATHEMATICS > Topology. Topology
Online-Zugang:	Volltext
Zusammenfassung:	A Guide to Topology is an introduction to basic topology. It covers point-set topology as well as Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful research too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize.
Beschreibung:	Title from publishers bibliographic system (viewed on 30 Jan 2012).
Beschreibung:	1 online resource (1 online resource)
Bibliographie:	""Bibliography""""Index""; ""About the Author""
ISBN:	9780883859179 0883859173

Internformat

MARC


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505	0		\|a Preface -- Contents -- 1 Fundamentals -- 1.1 What is Topology? -- 1.2 First Definitions -- 1.3 Mappings -- 1.4 The Separation Axioms -- 1.5 Compactness -- 1.6 Homeomorphisms -- 1.7 Connectedness -- 1.8 Path-Connectedness -- 1.9 Continua -- 1.10 Totally Disconnected Spaces -- 1.11 The Cantor Set -- 1.12 Metric Spaces -- 1.13 Metrizability -- 1.14 Baireâ€?s Theorem -- 1.15 Lebesgueâ€?s Lemma and Lebesgue Numbers -- 2 Advanced Properties of Topological Spaces -- 2.1 Basis and Subbasis -- 2.2 Product Spaces -- 2.3 Relative Topology
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Datensatz im Suchindex

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author	Krantz, Steven G. (Steven George), 1951-
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contents	Preface -- Contents -- 1 Fundamentals -- 1.1 What is Topology? -- 1.2 First Definitions -- 1.3 Mappings -- 1.4 The Separation Axioms -- 1.5 Compactness -- 1.6 Homeomorphisms -- 1.7 Connectedness -- 1.8 Path-Connectedness -- 1.9 Continua -- 1.10 Totally Disconnected Spaces -- 1.11 The Cantor Set -- 1.12 Metric Spaces -- 1.13 Metrizability -- 1.14 Baireâ€?s Theorem -- 1.15 Lebesgueâ€?s Lemma and Lebesgue Numbers -- 2 Advanced Properties of Topological Spaces -- 2.1 Basis and Subbasis -- 2.2 Product Spaces -- 2.3 Relative Topology 2.4 First Countable, Second Countable, and So Forth2.5 Compactifications -- 2.6 Quotient Topologies -- 2.7 Uniformities -- 2.8 Morse Theory -- 2.9 Proper Mappings -- 2.10 Paracompactness -- 3 Moore-Smith Convergence and Nets -- 3.1 Introductory Remarks -- 3.2 Nets -- 4 Function Spaces -- 4.1 Preliminary Ideas -- 4.2 The Topology of Pointwise Convergence -- 4.3 The Compact-Open Topology -- 4.4 Uniform Convergence -- 4.5 Equicontinuity and the Ascoli-Arzela Theorem -- 4.6 The Weierstrass Approximation Theorem -- Table of Notation -- Glossary
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spelling	Krantz, Steven G. (Steven George), 1951- https://id.oclc.org/worldcat/entity/E39PBJw8VQ7cxG48KCfPym3RKd http://id.loc.gov/authorities/names/n81051364 A Guide to Topology / Steven G. Krantz. Cambridge : Cambridge University Press, 2012. 1 online resource (1 online resource) text txt rdacontent computer c rdamedia online resource cr rdacarrier Dolciani Mathematical Expositions ; v. 40 Title from publishers bibliographic system (viewed on 30 Jan 2012). ""Bibliography""""Index""; ""About the Author"" Preface -- Contents -- 1 Fundamentals -- 1.1 What is Topology? -- 1.2 First Definitions -- 1.3 Mappings -- 1.4 The Separation Axioms -- 1.5 Compactness -- 1.6 Homeomorphisms -- 1.7 Connectedness -- 1.8 Path-Connectedness -- 1.9 Continua -- 1.10 Totally Disconnected Spaces -- 1.11 The Cantor Set -- 1.12 Metric Spaces -- 1.13 Metrizability -- 1.14 Baireâ€?s Theorem -- 1.15 Lebesgueâ€?s Lemma and Lebesgue Numbers -- 2 Advanced Properties of Topological Spaces -- 2.1 Basis and Subbasis -- 2.2 Product Spaces -- 2.3 Relative Topology 2.4 First Countable, Second Countable, and So Forth2.5 Compactifications -- 2.6 Quotient Topologies -- 2.7 Uniformities -- 2.8 Morse Theory -- 2.9 Proper Mappings -- 2.10 Paracompactness -- 3 Moore-Smith Convergence and Nets -- 3.1 Introductory Remarks -- 3.2 Nets -- 4 Function Spaces -- 4.1 Preliminary Ideas -- 4.2 The Topology of Pointwise Convergence -- 4.3 The Compact-Open Topology -- 4.4 Uniform Convergence -- 4.5 Equicontinuity and the Ascoli-Arzela Theorem -- 4.6 The Weierstrass Approximation Theorem -- Table of Notation -- Glossary A Guide to Topology is an introduction to basic topology. It covers point-set topology as well as Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful research too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize. Topology. http://id.loc.gov/authorities/subjects/sh85136089 Topologie. MATHEMATICS Topology. bisacsh Topology fast Print version: Krantz, Steven G. Guide to Topology. Washington : Mathematical Association of America, ©2014 9780883853467 Dolciani mathematical expositions. http://id.loc.gov/authorities/names/n42009859 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450275 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450275 Volltext
spellingShingle	Krantz, Steven G. (Steven George), 1951- A Guide to Topology / Dolciani mathematical expositions. Preface -- Contents -- 1 Fundamentals -- 1.1 What is Topology? -- 1.2 First Definitions -- 1.3 Mappings -- 1.4 The Separation Axioms -- 1.5 Compactness -- 1.6 Homeomorphisms -- 1.7 Connectedness -- 1.8 Path-Connectedness -- 1.9 Continua -- 1.10 Totally Disconnected Spaces -- 1.11 The Cantor Set -- 1.12 Metric Spaces -- 1.13 Metrizability -- 1.14 Baireâ€?s Theorem -- 1.15 Lebesgueâ€?s Lemma and Lebesgue Numbers -- 2 Advanced Properties of Topological Spaces -- 2.1 Basis and Subbasis -- 2.2 Product Spaces -- 2.3 Relative Topology 2.4 First Countable, Second Countable, and So Forth2.5 Compactifications -- 2.6 Quotient Topologies -- 2.7 Uniformities -- 2.8 Morse Theory -- 2.9 Proper Mappings -- 2.10 Paracompactness -- 3 Moore-Smith Convergence and Nets -- 3.1 Introductory Remarks -- 3.2 Nets -- 4 Function Spaces -- 4.1 Preliminary Ideas -- 4.2 The Topology of Pointwise Convergence -- 4.3 The Compact-Open Topology -- 4.4 Uniform Convergence -- 4.5 Equicontinuity and the Ascoli-Arzela Theorem -- 4.6 The Weierstrass Approximation Theorem -- Table of Notation -- Glossary Topology. http://id.loc.gov/authorities/subjects/sh85136089 Topologie. MATHEMATICS Topology. bisacsh Topology fast
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title	A Guide to Topology /
title_auth	A Guide to Topology /
title_exact_search	A Guide to Topology /
title_full	A Guide to Topology / Steven G. Krantz.
title_fullStr	A Guide to Topology / Steven G. Krantz.
title_full_unstemmed	A Guide to Topology / Steven G. Krantz.
title_short	A Guide to Topology /
title_sort	guide to topology
topic	Topology. http://id.loc.gov/authorities/subjects/sh85136089 Topologie. MATHEMATICS Topology. bisacsh Topology fast
topic_facet	Topology. Topologie. MATHEMATICS Topology. Topology
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