A Topological Aperitif

Front Cover
Springer Science & Business Media, 2001 - Mathematics - 166 pages
This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology.After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory.There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study."A Topological Aperitif provides a marvellous introduction to the subject, with many different tastes of ideas.Stephen Huggett and David Jordan have excellent credentials for explaining the beauty of this curiously austere but potentially enormously general form of geometry".Professor Sir Roger Penrose OM FRS, Mathematical Institute, Oxford, UK
 

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Contents

Homeomorphic Sets
1
Topological Properties
17
Equivalent Subsets
29
Surfaces and Spaces
61
Polyhedra
77
Winding Number
103
Continuity
117
Knots
125
History
133
Solutions
139
Bibliography
163
Index
165
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