Nagata / de Bruijn / de Groot Modern General Topology

2. Auflage 2014
ISBN: 978-1-4832-7816-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 376 Seiten, Web PDF

Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and approaches employed in pure and applied mathematics, including spaces, cardinal and ordinal numbers, and mappings. The publication first elaborates on set, cardinal and ordinal numbers, basic concepts in topological spaces, and various topological spaces. Discussions focus on metric space, axioms of countability, compact space and paracompact space, normal space and fully normal space, subspace, product space, quotient space, and inverse limit space, convergence, mapping, and open basis and neighborhood basis. The book then ponders on compact spaces and related topics, as well as product of compact spaces, compactification, extensions of the concept of compactness, and compact space and the lattice of continuous functions. The manuscript tackles paracompact spaces and related topics, metrizable spaces and related topics, and topics related to mappings. Topics include metric space, paracompact space, and continuous mapping, theory of inverse limit space, theory of selection, mapping space, imbedding, metrizability, uniform space, countably paracompact space, and modifications of the concept of paracompactness. The book is a valuable source of data for mathematicians and researchers interested in modern general topology.

Autoren/Hrsg.

Nagata, Jun-Iti

de Bruijn, N. G.

de Groot, J.

Zaanen, A. C.

Inhaltsverzeichnis

1;Front Cover;1
2;Modern General Topology;4
3;Copyright Page;5
4;Table of Contents;10
5;PREFACE;6
6;PREFACE TO THE SECOND EDITION;8
7;CHAPTER I. INTRODUCTION;12
7.1;1. Set;12
7.2;2. Cardinal numbers;16
7.3;3. Ordinal numbers;20
7.4;4. Zermelo's theorem and Zom's lemma;26
7.5;5. Topology of Euclidean plane;33
7.6;Exercise I;39
8;CHAPTER II. BASIC CONCEPTS IN TOPOLOGICAL SPACES;41
8.1;1. Topological space;41
8.2;2. Open basis and neighborhood basis;46
8.3;3. Closure;49
8.4;4. Convergence;54
8.5;5. Covering;59
8.6;6. Mapping;63
8.7;7. Subspace, product space, quotient space and inverse limit space;67
8.8;8. Connectedness;73
8.9;Exercise II;76
9;CHAPTER III. VARIOUS TOPOLOGICAL SPACES;80
9.1;1. T1, T2, regular and completely regular spaces;80
9.2;2. Normal space and fully normal space;83
9.3;3. Compact space and paracompact space;94
9.4;4. Axioms of countability;100
9.5;5. Metric space;104
9.6;Exercise III;114
10;CHAPTER IV. COMPACT SPACES AND RELATED TOPICS;117
10.1;1. Product of compact spaces;117
10.2;2. Compactification;126
10.3;3. Compact space and the lattice of continuous functions;143
10.4;4. Extensions of the concept of compactness;150
10.5;Exercise IV;158
11;CHAPTER V. PARACOMPACT SPACES AND RELATED TOPICS;160
11.1;1. Fundamental theorem;160
11.2;2. Further properties of paracompact spaces;165
11.3;3. Countably paracompact space;175
11.4;4. Modifications of the concept of paracompactness;181
11.5;5. Characterization by product spaces;185
11.6;Exercise V;193
12;CHAPTER VI. METRIZABLE SPACES AND RELATED TOPICS;195
12.1;1. Metrlzability;195
12.2;2. Imbedding;219
12.3;3. Union and image of metrizable spaces;224
12.4;4. Uniform space;232
12.5;5. Proximity space;251
12.6;6. P-spaces;263
12.7;Exercise VI;281
13;CHAPTER VII. TOPICS RELATED TO MAPPINGS;284
13.1;1. Mapping space;284
13.2;2. Metric space, paracompact space and continuous mapping;301
13.3;3. Theory of inverse limit space;316
13.4;4. Theory of selection;328
13.5;Exercise VII;350
14;EPILOGUE;353
15;BIBLIOGRAPHY;355
16;INDEX;371