Nagata Modern General Topology

3. Auflage 1985
ISBN: 978-0-08-093379-5
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 521 Seiten

This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first edition appeared.
The reader will find many new topics in chapters IV-VIII, e.g. theory of Wallmann-Shanin's compactification, realcompact space, various generalizations of paracompactness, generalized metric spaces, Dugundji type extension theory, linearly ordered topological space, theory of cardinal functions, dyadic space, etc., that were, in the author's opinion, mostly special or isolated topics some twenty years ago but now settle down into the mainstream of general topology.

Autoren/Hrsg.

Nagata, J. -I.

Inhaltsverzeichnis

1;Front Cover;1
2;Modern General Topology;4
3;Copyright Page;5
4;Contents;10
5;Chapter I. Introduction;12
5.1;1. Set ;12
5.2;2. Cardinal numbers ;16
5.3;3. Ordinal numbers ;21
5.4;4. Zermelo’s theorem and Zorn’s lemma;27
5.5;5. Topology of Euclidean plane ;34
5.6;Exercise I ;41
6;Chapter II. Basic Concepts in Topological Spaces;43
6.1;1. Topological space ;43
6.2;2. Open basis and neighborhood basis ;49
6.3;3. Closure ;52
6.4;4. Convergence ;58
6.5;5. Covering ;63
6.6;6. Mapping ;67
6.7;7. Subspace, product space, quotient space and inverse limit space ;71
6.8;8. Connectedness ;79
6.9;Exercise II ;83
7;Chapter III. Various Topological Spaces;88
7.1;1. T1, T2, regular and completely regular spaces ;88
7.2;2. Normal space and fully normal space ;93
7.3;3. Compact space and paracompact space;107
7.4;4. Axioms of countability ;115
7.5;5. Metric space ;120
7.6;Exercise IIII ;131
8;Chapter IV. Compact Spaces and Related Topics;135
8.1;1. Product of compact spaces ;135
8.2;2. Compactification ;147
8.3;3. More of compactifications ;156
8.4;4. Compact space and the lattice of continuous functions ;168
8.5;5. Extensions of the concept of compactness;179
8.6;6. Realcompact space ;185
8.7;Exercise IV ;196
9;Chapter V. Paracompact Spaces and Related Topics;199
9.1;1. Fundamental theorem ;199
9.2;2. Further properties of paracompact spaces ;205
9.3;3. Countably paracompact space and collectionwise normal space ;216
9.4;4. Modifications of the concept of paracompactness ;225
9.5;5. Characterization by product spaces ;234
9.6;Exercise V ;252
10;Chapter VI. Metrizable Spaces and Related Topics;255
10.1;1. Metrizability ;255
10.2;2. Complete metrizability ;275
10.3;3. Imbedding ;280
10.4;4. Union and image of metrizable spaces ;286
10.5;5. Uniform space ;295
10.6;6. Proximity space ;316
10.7;7. P-space ;327
10.8;8. Various generalized metric spaces ;347
10.9;Exercise VI ;369
11;Chapter VII. Topics Related to Mappings;372
11.1;1. Mapping space;372
11.2;2. Metric space, paracompact space and continuous mapping ;392
11.3;3. Metrization of M-spaces ;412
11.4;4. Theory of inverse limit space ;419
11.5;5. Theory of selection;434
11.6;6. More of extension theory ;454
11.7;7. Characterization of topological properties in terms of C(X);459
11.8;Exercise VII;464
12;Chapter VIII. Other Aspects;467
12.1;1. Linearly ordered space ;467
12.2;2. Cardinal functions ;478
12.3;3. Dyadic space ;487
12.4;4. Measure and topological space ;493
12.5;Exercise VIII ;504
13;Epilogue;506
14;Bibliography;507
15;Index;528