A First Course in Algebraic Topology

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CUP Archive, Sep 25, 1980 - Mathematics - 269 pages
1 Review
This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.
 

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Contents

Sets and groups
1
metric spaces
6
Topological spaces
11
Continuous functions
16
Induced topology
20
Quotient topology and groups acting on spaces
27
Product spaces
39
Compact spaces
44
The fundamental group
124
The fundamental group of a circle
135
Covering spaces
143
The fundamental group of a covering space
151
The fundamental group of an orbit space
154
The BorsukUlam and hamsandwich theorems
157
lifting theorems
162
existence theorems
170

Hausdorff spaces
50
Connected spaces
58
The pancake problems
63
Manifolds and surfaces
68
Paths and path connected spaces
93
12A The Jordan curve theorem
100
Homotopy of continuous mappings
110
Multiplication of paths
118
I Generators
176
II Relations
187
III Calculations
194
The fundamental group of a surface
202
I Background and torus knots
209
II Tame knots
221
28A Table of knots
234
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