From Geometry to Topology

Frontcover
Courier Dover Publications, 1974 - 186 Seiten
3 Rezensionen
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4–12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition.
  

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Inhalt

Congruence Classes
1
NonEuclidean Geometries
9
From Geometry to Topology
17
Surfaces
20
Connectivity
33
Euler Characteristic
40
Networks
58
The Colouring of Maps
70
Fixed Point Theorems
84
Plane Diagrams
90
The Standard Model
101
Continuity
117
The Language of Sets
125
Functions
134
Metric Spaces
150
Topological Spaces
156

The Jordan Curve Theorem
78

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