A Taste of Topology

Front Cover
Springer Science & Business Media, Dec 7, 2007 - Mathematics - 182 pages
1 Review

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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

IV
5
VI
13
VII
17
VIII
20
IX
23
XI
28
XII
34
XIII
40
XXII
107
XXIII
109
XXV
116
XXVI
121
XXVII
129
XXVIII
133
XXX
148
XXXI
154

XIV
52
XV
59
XVI
61
XVIII
72
XIX
79
XX
89
XXI
100
XXXII
157
XXXIII
161
XXXIV
165
XXXV
169
XXXVI
171
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information