Basic Topology

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Springer Science & Business Media, Apr 9, 2013 - Mathematics - 251 pages
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties will help students gain a rounded understanding of the subject.
 

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Contents

Preface
1
Continuity
27
A spacefilling curve
36
Compactness and connectedness
43
Identification spaces
65
The identification topology
74
Orbit spaces
81
The fundamental group
87
27
143
Surfaces
149
Simplicial homology
173
Degree and Lefschetz number
195
Knots and covering spaces
213
43
227
Generators and relations
241
47
246

Triangulations
119
i
123

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