Taste of Topology

Name: Taste of Topology
Availability: InStock
ISBN: 9780387257907

ISBN-10: 038725790X

ISBN-13: 9780387257907

Edition: 2005

Authors: Volker Runde

List price: $59.99

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Description:

If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students canbenefit from some parts. Great care has been devoted to the selection of examples that are not…

Book details

List price: $59.99
Copyright year: 2005
Publisher: Springer New York
Publication date: 7/6/2005
Binding: Paperback
Pages: 177
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 0.836
Language: English



Preface


Introduction



Set Theory



Sets and Functions



Cardinals



Cartesian Products


Remarks



Metric Spaces



Definitions and Examples



Open and Closed Sets



Convergence and Continuity



Completeness



Compactness for Metric Spaces


Remarks



Set-Theoretic Topology



Topological Spaces-Definitions and Examples



Continuity and Convergence of Nets



Compactness



Connectedness



Separation Properties


Remarks



Systems of Continuous Functions



Urysohn's Lemma and Applications



The Stone-&Ccaron;ech Compactification



The Stone-Weierstraï¿½ Theorems


Remarks



Basic Algebraic Topology



Homotopy and the Fundamental Group



Covering Spaces


Remarks



The Classical Mittag-Leffler Theorem Derived from Bourbaki's



Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces



The Arzelï¿½-Ascoli Theorem


References


Index