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9780486427867

Invitation to Combinatorial Topology

by ; ;
  • ISBN13:

    9780486427867

  • ISBN10:

    0486427862

  • Format: Paperback
  • Copyright: 2003-03-14
  • Publisher: Dover Publications
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Supplemental Materials

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Summary

An elementary text that can be understood by anyone with a background in high school geometry, this text focuses on the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, more. Includes 108 figures. 1967 edition.

Table of Contents

Foreword v
Translator's Preface ix
Topological Generalities
Qualitative Geometric Properties
1(1)
Coloring Geographical Maps
2(3)
The Problem of Neighboring Regions
5(1)
Topology, India-Rubber Geometry
6(1)
Homeomorphism
7(4)
Topology, Continuous Geometry
11(1)
Comparison of Elementary Geometry, Projective Geometry, and Topology
12(2)
Relative Topological Properties
14(3)
Set Topology and Combinatorial Topology
17(2)
The Development of Topology
19(2)
Topological Notions About Surfaces
Descartes' Theorem
21(4)
An Application of Descartes' Theorem
25(2)
Characteristic of a Surface
27(2)
Unilateral Surfaces
29(2)
Orientability and Nonorientability
31(4)
Topological Polygons
35(1)
Construction of Closed Orientable Surfaces from Polygons by Identifying Their Sides
36(4)
Construction of Closed Nonorientable Surfaces from Polygons by Identifying Their Sides
40(5)
Topological Definition of a Closed Surface
45(4)
Topological Classification of Closed Surfaces
The Principal Problem in the Topology of Surfaces
49(1)
Planar Polygonal Schema and Symbolic Representation of a Polyhedron
50(3)
Elementary Operations
53(2)
Use of Normal Forms of Polyhedra
55(1)
Reduction to Normal Form: I
56(3)
Reduction to Normal Form: II
59(5)
Characteristic and Orientability
64(3)
The Principal Theorem of the Topology of Closed Surfaces
67(2)
Application to the Geometric Theory of Functions
69(1)
Genus and Connection Number of Closed Orientable Surfaces
69(4)
Bibliography 73(2)
Translator's Notes 75(45)
Index 120

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