From Geometry To Topology

H.Graham Flegg

186 pages, parution le 09/01/2002

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Résumé

Unlike most other introductions to topology-which tend to plunge students so quickly into a formalized and abstract presentation of concepts that it is impossible for them to get any real feel for the subject-this volume surveys these concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology.

Laying the foundations for this bridge, 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, including surfaces, connectivity, the Euler characteristic, networks, the coloring of maps, the Jordan curve theorem, fixed Point theorems, plane diagrams, and the standard model. In the remaining five chapters, the author moves to a more conventîop.4~l presentation, enlarging on the concept of continuity and introducing sets, functions, metric spaces, and topological spaces. Exercises and problems are included at the end of the text.

In addition to its value as an initiation into the formal study of topology for prospective and first-year mathematics students, this volume is also ideal for any reader wishing to discover and appreciate the beauty and fascination of a relatively modern branch of mathematics.

Contents

Author's Preface

Acknowledgements

Congruence Classes
Non-Euclidean Geometries
From Geometry to Topology
Surfaces
Connectivity
Euler Characteristic
Networks
The Colouring of Maps
The Jordan Curve Theorem
Fixed Point Theorems
Plane Diagrams
The Standard Model
Continuity
The language of Sets
Functions
Metric Spaces
Topological Spaces

Historical Note

Excercises and Problems

Bibliography

Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	H.Graham Flegg
Parution	09/01/2002
Nb. de pages	186
Format	13,8 x 21,5
Couverture	Broché
Poids	219g
Intérieur	Noir et Blanc
EAN13	9780486419619
ISBN13	978-0-486-41961-9