Introduction to topology / Theodore W. Gamelin and Robert Everist Greene.
Editor: Mineola, N.Y. : Dover Publications, 1999Edición: 2nd edDescripción: xii, 234 p. : il. ; 24 cmISBN: 0486406806 (pbk.)Tema(s): TopologyOtra clasificación: 54-01 (55-01)CONTENTS ONE METRIC SPACES [1] 1. Open and closed sets [2] 2. Completeness [9] 3. The real line [13] 4. Products of metric spaces [16] 5. Compactness [19] 6. Continuous functions [26] 7. Normed linear spaces [30] 8. The contraction principle [39] 9. The Frechet derivative [47] TWO TOPOLOGICAL SPACES [59] 1. Topological spaces [60] 2. Subspaces [64] 3. Continuous functions [65] 4. Base for a topology [69] 5. Separation axioms [72] 6. Compactness [78] 7. Locally compact spaces [83] 8. Connectedness [85] 9. Path connectedness [89] 10. Finite product spaces [91] 11. Set theory and Zorn’s lemma [96] 12. Infinite product spaces [99] 13. Quotient spaces [104] THREE HOMOTOPY THEORY [109] 1. Groups [109] 2. Homotopic paths [112] 3. The fundamental group [118] 4. Induced homomorphisms [122] 5. Covering spaces [124] 6. Some applications of the index [132] 7.Homotopic maps [136] 8. Maps into the punctured plane [141] 9. Vector fields [146] 10. The Jordan Curve Theorem [153] FOUR HIGHER DIMENSIONAL HOMOTOPY [161] 1. Higher homotopy groups [162] 2. Noncontractibility of Sn [166] 3. Simplexes and barycentric subdivision [171] 4. Approximation by piecewise linear maps [178] 5. Degrees of maps [182] BIBLIOGRAPHY [192] LIST OF NOTATIONS [193] SOLUTIONS TO SELECTED EXERCISES [195]
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An unabridged reprint of the first edition published by W.B. Saunders Company, Philadelphia in 1983. A new addendum has been added.
Incluye referencias bibliográficas (p. 192) e índice.
CONTENTS --
ONE --
METRIC SPACES [1] --
1. Open and closed sets [2] --
2. Completeness [9] --
3. The real line [13] --
4. Products of metric spaces [16] --
5. Compactness [19] --
6. Continuous functions [26] --
7. Normed linear spaces [30] --
8. The contraction principle [39] --
9. The Frechet derivative [47] --
TWO --
TOPOLOGICAL SPACES [59] --
1. Topological spaces [60] --
2. Subspaces [64] --
3. Continuous functions [65] --
4. Base for a topology [69] --
5. Separation axioms [72] --
6. Compactness [78] --
7. Locally compact spaces [83] --
8. Connectedness [85] --
9. Path connectedness [89] --
10. Finite product spaces [91] --
11. Set theory and Zorn’s lemma [96] --
12. Infinite product spaces [99] --
13. Quotient spaces [104] --
THREE --
HOMOTOPY THEORY [109] --
1. Groups [109] --
2. Homotopic paths [112] --
3. The fundamental group [118] --
4. Induced homomorphisms [122] --
5. Covering spaces [124] --
6. Some applications of the index [132] --
7.Homotopic maps [136] --
8. Maps into the punctured plane [141] --
9. Vector fields [146] --
10. The Jordan Curve Theorem [153] --
FOUR HIGHER DIMENSIONAL HOMOTOPY [161] --
1. Higher homotopy groups [162] --
2. Noncontractibility of Sn [166] --
3. Simplexes and barycentric subdivision [171] --
4. Approximation by piecewise linear maps [178] --
5. Degrees of maps [182] --
BIBLIOGRAPHY [192] --
LIST OF NOTATIONS [193] --
SOLUTIONS TO SELECTED EXERCISES [195] --
MR, 2000c:54001
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