Dimension theory of general spaces

DIMENSION THEORY OF GENERAL SPACES......Page 1
Half-title......Page 2
Title Page......Page 3
Copyright Page......Page 4
Contents......Page 6
Introduction......Page 10
1 Topological spaces......Page 14
2 Local finiteness, the weak topology and the weight of topological spaces......Page 23
3 Normal Spaces......Page 30
4 Complete, total and perfect normality......Page 40
5 Compact and completely regular spaces......Page 48
6 Bicompactifications......Page 55
7 Inverse limits......Page 65
1 Paracompact spaces......Page 70
2 Hereditarily paracompact spaces, weakly, strongly and completely paracompact spaces......Page 85
3 Pseudo -metrizable and metrizable spaces......Page 90
4 Completeness and the spaces C[sub(n)](X)......Page 104
5 Perfect mappings......Page 106
6 Simplicial complexes, polyhedra and the nerves of coverings......Page 118
Notes......Page 123
1 The definition of dim......Page 124
2 The dimension of Euclidean space......Page 134
3 Inessential mappings and unstable values......Page 140
4 Locally finite coverings......Page 143
5 Sum theorems......Page 148
6 The monotonicity of covering dimension......Page 151
7 The dimension of polyhedra......Page 155
8 Rank and Dimension......Page 157
Notes......Page 160
1 Small inductive dimension......Page 163
2 Large inductive dimension......Page 168
3 Two examples......Page 174
4 Subset and sum theorems......Page 179
5 Dimension of pseudo-metrizable spaces......Page 191
Notes......Page 198
1 Definitions and relations with dimension......Page 201
2 Subset and sum theorems......Page 203
3 The monotonicity of covering dimension......Page 206
4 Some examples......Page 211
Notes......Page 226
1 Canonical coverings and dimension......Page 227
2 Irreducible mappings......Page 231
3 Images of zero-dimensional spaces......Page 234
4 Dimension and bicompactification......Page 244
Notes......Page 251
1 Images of zero-dimensional spaces......Page 252
2 Sequences of open coverings and inverse limits......Page 263
3 Universal spaces for metrizable spaces of given weight and dimension......Page 270
4 Prabir Roy\'s example......Page 284
5 Generalizations of metric spaces and dimension theory......Page 301
Notes......Page 308
1 Inverse limits......Page 311
2 A family of examples due to Vopěnka......Page 315
3 V. V. Filippov\'s example......Page 321
Notes......Page 343
1 Mappings into spheres......Page 345
2 Mappings and dimension......Page 349
3 The product theorem for covering dimension......Page 363
4 The product theorem for large inductive dimension......Page 368
Notes......Page 375
1 A modification of covering dimension......Page 379
2 Normed algebras......Page 382
3 Dimension and bicompactification......Page 391
4 Analytic dimension......Page 400
5 Z-spaces......Page 414
Notes......Page 423
Bibliography......Page 428
Index......Page 437
Back Cover......Page 442