A Taste of Topology

Volker Runde - Collection Universitext

176 pages, parution le 23/08/2005

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Résumé

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 self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis.

In some points, the book treats its material differently than other texts on the subject:

Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem;
nets are used extensively, in particular for an intuitive proof of Tychonoff's theorem;
a short and elegant, but little known proof for the Stone-Weierstrass theorem is given.

Sommaire

Preface
Introduction
Set Theory
Metric Spaces
Set Theoretic Topology
Systems of Continuous Functions
Basic Algebraic Topology
The Classical Mittag-Leffler Theorem Derived from Bourbaki's
Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces
The Arzela-Ascoli Theorem
References
List of Symbols
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Volker Runde
Collection	Universitext
Parution	23/08/2005
Nb. de pages	176
Format	15,5 x 23,5
Couverture	Broché
Poids	278g
Intérieur	Noir et Blanc
EAN13	9780387257907
ISBN13	978-0-387-25790-7