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Sigma Series in Pure Mathematics -- Volume 6

   Enlarged Picture

Ryszard Engelking

General Topology

540 pages, hard cover, ISBN 3-88538-006-4, EUR 75.00, 1989

This book is an encyclopedia for General Topology. It emerged from several former editions and is today the most complete source and reference book for General Topology. It is indispensable for every library and belongs onto the table of every working topologist.

"This new edition deserves the same praise as the first one ... heartily recommended ... I cannot but heartily recommend it to anyone with some interest in General Topology." (Zentralblatt f. Mathematik, K.P.Hart).


Zentralblatt-Review


Contents:

Preface to the first edition vii
Preface to the revised edition viii
     
  Introduction  
I.1 Algebra of sets. Functions 1
I.2 Cardinal numbers 3
I.3 Order relations. Ordinal numbers 4
I.4 The axiom of choice 8
I.5 Real numbers 10
     
  Chapter 1: Topological spaces  
1.1 Topological spaces. Open and closed sets. Bases. Closure and interior of a set 11
1.2 Methods of generating topologies 20
1.3 Boundary of a set and derived set. Dense and nowhere dense sets. Borel sets 24
1.4 Continuous mappings. Closed and open mappings. Homeomorphisms 27
1.5 Axioms of separation 36
1.6 Convergence in topological spaces: Nets and filters. Sequential and Fréchet spaces 49
1.7 Problems 56
     
  Chapter 2: Operations on topological spaces  
2.1 Subspaces 65
2.2 Sums 74
2.3 Cartesian products 77
2.4 Quotient spaces and quotient mappings 90
2.5 Limits of inverse systems 98
2.6 Function spaces I: The topology of uniform convergence on RX and the topology of pointwise convergence 105
2.7 Problems 112
     
  Chapter 3: Compact spaces  
3.1 Compact spaces 123
3.2 Operations on compact spaces 136
3.3 Locally compact spaces and k-spaces 148
3.4 Function spaces II: The compact-open topology 156
3.5 Compactifications 166
3.6 The Cech-Stone compactification and the Wallman extension 172
3.7 Perfect mappings 182
3.8 Lindelöf spaces 192
3.9 Cech-complete spaces 196
3.10 Countably compact spaces, pseudocompact spaces and sequentially compact spaces 202
3.11 Realcompact spaces 214
3.12 Problems 220
     
  Chapter 4: Metric and metrizable spaces  
4.1 Metric and metrizable spaces 248
4.2 Operations on metrizable spaces 258
4.3 Totally bounded and complete metric spaces. Compactness in metric spaces 266
4.4 Metrization theorems I 280
4.5 Problems 288
     
  Chapter 5: Paracompact spaces  
5.1 Paracompact spaces 299
5.2 Countably paracompact spaces 316
5.3 Weakly and strongly paracompact spaces 322
5.4 Metrization theorems II 329
5.5 Problems 337
     
  Chapter 6: Connected spaces  
6.1 Connected spaces 352
6.2 Various kinds of disconnectedness 360
6.3 Problems 372
     
  Chapter 7: Dimension of topological spaces  
7.1 Definitions and basic properties of dimensions ind, Ind, and dim 383
7.2 Further properties of the dimension dim 394
7.3 Dimension of metrizable spaces 402
7.4 Problems 418
     
  Chapter 8: Uniform spaces and proximity spaces  
8.1 Uniformities and uniform spaces 426
8.2 Operations on uniform spaces 438
8.3 Totally bounded and complete uniform spaces. Compactness in uniform spaces 444
8.4 Proximities and proximity spaces 451
8.5 Problems 460
     
Bibliography 469
     
  Tables  
  Relations between main classes of topological spaces 508
  Invariants of operations 509
  Invariants and inverse invariants of mappings 510
     
List of special symbols 511
Author index 514
Subject index 520