Foundations of topology/ C. Wayne Patty.

By: Patty, C.WayneMaterial type: TextTextSeries: Jones and Bartlett Publishers series in mathematics., TopologyPublication details: Boston: Jones and Bartlett, 2013Edition: 2nd edDescription: xi, 380 p. : ill. ; 24 cmISBN: 9780763742348Subject(s): Topology DDC classification: 514
Contents:
1 Topological Spaces 1 1 Metric Spaces 1 2 Topological Spaces: The Definition and Examples 10 3 Basis for a Topology 15 4 Closed Sets, Closures, and Interiors of Sets 26 5 Metric Spaces Revisited 36 6 Convergence 42 7 Continuous Functions and Homeomorphisms 50 2 New Spaces from Old Ones 59 1 Subspaces 59 2 The Product Topology on X ? Y 67 3 The Product Topology 73 4 The Weak Topology and the Product Topology 80 5 The Uniform Metric 85 6 Quotient Spaces 90 3 Connectedness 102 1 Connected Spaces 102 2 Pathwise and Local Connectedness 112 3 Totally Disconnected Spaces 119 4 Compactness 123 1 Compactness in Metric Spaces 123 2 Compact Spaces 131 3 Local Compactness and the Relation Between Various Forms of Compactness 140 4 The Weak Topology on a Topological Space 145 5 Equicontinuity 149 5 The Separation and Countability Axioms 154 1 T0-, T1-, and T2-Spaces 154 2 Regular and Completely Regular Spaces 159 3 Normal and Completely Normal Spaces 167 4 The Countability Axioms 172 5 Urysohn¿s Lemma and the Tietze Extension Theorem 176 6 Embeddings 180 6 Special Topics 185 1 Contraction Mappings in Metric Spaces 185 2 Normed Linear Spaces 187 3 The Fréchet Derivative 192 4 Manifolds 199 5 Fractals 210 6 Compactifications 218 7 The Alexander Subbase and the Tychonoff Theorems 225 7 Metrizability and Paracompactness 229 1 Urysohn¿s Metrization Theorem 229 2 Paracompactness 232 3 The Nagata-Smirnov Metrization Theorem 241 8 The Fundamental Group and Covering Spaces 248 1 Homotopy of Paths 248 2 The Fundamental Group 257 3 The Fundamental Group of the Circle 261 4 Covering Spaces 265 5 Applications and Additional Examples of Fundamental Groups 268 6 Knots 274 9 Applications of Homotopy 281 1 Inessential Maps 281 2 The Fundamental Theorem of Algebra 283 3 Homotopic Maps 285 4 The Jordan Curve Theorem 287 A Logic and Proofs 294 B Sets 300 C Functions 305 D Indexing Sets and Cartesian Products 311 E Equivalence Relations and Order Relations 315 F Countable Sets 320 G Uncountable Sets 324 H Ordinal and Cardinal Numbers 326 I Algebra 331 Bibliography 338 Index 340
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
General Books General Books Central Library, Sikkim University
General Book Section
514 PAT/F (Browse shelf(Opens below)) Available P40953
Total holds: 0

1 Topological Spaces 1
1 Metric Spaces 1
2 Topological Spaces: The Definition and Examples 10
3 Basis for a Topology 15
4 Closed Sets, Closures, and Interiors of Sets 26
5 Metric Spaces Revisited 36
6 Convergence 42
7 Continuous Functions and Homeomorphisms 50
2 New Spaces from Old Ones 59
1 Subspaces 59
2 The Product Topology on X ? Y 67
3 The Product Topology 73
4 The Weak Topology and the Product Topology 80
5 The Uniform Metric 85
6 Quotient Spaces 90
3 Connectedness 102
1 Connected Spaces 102
2 Pathwise and Local Connectedness 112
3 Totally Disconnected Spaces 119
4 Compactness 123
1 Compactness in Metric Spaces 123
2 Compact Spaces 131
3 Local Compactness and the Relation Between Various Forms of Compactness 140
4 The Weak Topology on a Topological Space 145
5 Equicontinuity 149
5 The Separation and Countability Axioms 154
1 T0-, T1-, and T2-Spaces 154
2 Regular and Completely Regular Spaces 159
3 Normal and Completely Normal Spaces 167
4 The Countability Axioms 172
5 Urysohn¿s Lemma and the Tietze Extension Theorem 176
6 Embeddings 180
6 Special Topics 185
1 Contraction Mappings in Metric Spaces 185
2 Normed Linear Spaces 187
3 The Fréchet Derivative 192
4 Manifolds 199
5 Fractals 210
6 Compactifications 218
7 The Alexander Subbase and the Tychonoff Theorems 225
7 Metrizability and Paracompactness 229
1 Urysohn¿s Metrization Theorem 229
2 Paracompactness 232
3 The Nagata-Smirnov Metrization Theorem 241
8 The Fundamental Group and Covering Spaces 248
1 Homotopy of Paths 248
2 The Fundamental Group 257
3 The Fundamental Group of the Circle 261
4 Covering Spaces 265
5 Applications and Additional Examples of Fundamental Groups 268
6 Knots 274
9 Applications of Homotopy 281
1 Inessential Maps 281
2 The Fundamental Theorem of Algebra 283
3 Homotopic Maps 285
4 The Jordan Curve Theorem 287
A Logic and Proofs 294
B Sets 300
C Functions 305
D Indexing Sets and Cartesian Products 311
E Equivalence Relations and Order Relations 315
F Countable Sets 320
G Uncountable Sets 324
H Ordinal and Cardinal Numbers 326
I Algebra 331
Bibliography 338
Index 340

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