A Taste of Topology (Universitext) - Softcover

Runde, Volker

Softcover

ISBN 10: 038725790X ISBN 13: 9780387257907

Publisher: Springer, 2005

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2005
• Language: English
• ISBN 10: 038725790X
• ISBN 13: 9780387257907
• Binding: Paperback
• Number of pages: 187