Introduction to Topology
Published on 28. March 2003
Book
Paperback/Softback
256 pages
978-0-486-40680-0 (ISBN)
Description
This volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
More details
Language
English
Place of publication
United States
Target group
College/higher education
Dimensions
Height: 151 mm
Width: 229 mm
Thickness: 15 mm
Weight
372 gr
ISBN-13
978-0-486-40680-0 (9780486406800)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Previous edition
T. W. Gamelin | Robert E. Greene
Introduction to Topology
Book
04/1983
Thomson Learning
€65.19
Article exhausted; check for reprint
Content
ONE METRIC SPACES
1 Open and closed sets
2 Completeness
3 The real line
4 Products of metric spaces
5 Compactness
6 Continuous functions
7 Normed linear spaces
8 The contraction principle
9 The Frechet derivative
TWO TOPOLOGICAL SPACES
1 Topological spaces
2 Subspaces
3 Continuous functions
4 Base for a topology
5 Separation axioms
6 Compactness
7 Locally compact spaces
8 Connectedness
9 Path connectedness
10 Finite product spaces
11 Set theory and Zorn's lemma
12 Infinite product spaces
13 Quotient spaces
THREE HOMOTOPY THEORY
1 Groups
2 Homotopic paths
3 The fundamental group
4 Induced homomorphisms
5 Covering spaces
6 Some applications of the index
7 Homotopic maps
8 Maps into the punctured plane
9 Vector fields
10 The Jordan Curve Theorem
FOUR HIGHER DIMENSIONAL HOMOTOPY
1 Higher homotopy groups
2 Noncontractibility of Sn
3 Simplexes and barycentric subdivision
4 Approximation by piecewise linear maps
5 Degrees of maps
BIBLIOGRAPHY
LIST OF NOTATIONS
SOLUTIONS TO SELECTED EXERCISES
INDEX
1 Open and closed sets
2 Completeness
3 The real line
4 Products of metric spaces
5 Compactness
6 Continuous functions
7 Normed linear spaces
8 The contraction principle
9 The Frechet derivative
TWO TOPOLOGICAL SPACES
1 Topological spaces
2 Subspaces
3 Continuous functions
4 Base for a topology
5 Separation axioms
6 Compactness
7 Locally compact spaces
8 Connectedness
9 Path connectedness
10 Finite product spaces
11 Set theory and Zorn's lemma
12 Infinite product spaces
13 Quotient spaces
THREE HOMOTOPY THEORY
1 Groups
2 Homotopic paths
3 The fundamental group
4 Induced homomorphisms
5 Covering spaces
6 Some applications of the index
7 Homotopic maps
8 Maps into the punctured plane
9 Vector fields
10 The Jordan Curve Theorem
FOUR HIGHER DIMENSIONAL HOMOTOPY
1 Higher homotopy groups
2 Noncontractibility of Sn
3 Simplexes and barycentric subdivision
4 Approximation by piecewise linear maps
5 Degrees of maps
BIBLIOGRAPHY
LIST OF NOTATIONS
SOLUTIONS TO SELECTED EXERCISES
INDEX