TY  - BOOK
AU  - Patty, C.Wayne.
TI  - Foundations of topology
SN  - 9780763742348
U1  - 514 
PY  - 2013///
CY  - Boston
PB  - Jones and Bartlett
KW  - Topology	
N1  - 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
ER  -