ENGLISH

A Taste of Topology

By Volker Runde

Book information

Publisher
Springer
Year
2005
ISBN
038725790X, 9780387257907
Language
english
Format
PDF
Filesize
2 MB (1680910 bytes)
Series
Universitext
Pages
182\183
Library
torrents.ru tech collections 2009-11-14
Time added
2010-02-18 13:16:04

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 can benefit 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.

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