Modern General Topology (eBook)

Jun-iti Nagata (Autor)

N. G. De Bruijn, J. De Groot, A. C. Zaanen (Herausgeber)

eBook Download: PDF

2014 | 2. Auflage
376 Seiten
Elsevier Science (Verlag)
978-1-4832-7816-2 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Modern General Topology 4
Copyright Page 5
Table of Contents 10
PREFACE 6
PREFACE TO THE SECOND EDITION 8
CHAPTER I. INTRODUCTION 12
1. Set 12
2. Cardinal numbers 16
3. Ordinal numbers 20
4. Zermelo's theorem and Zom's lemma 26
5. Topology of Euclidean plane 33
Exercise I 39
CHAPTER II. BASIC CONCEPTS IN TOPOLOGICAL SPACES 41
1. Topological space 41
2. Open basis and neighborhood basis 46
3. Closure 49
4. Convergence 54
5. Covering 59
6. Mapping 63
7. Subspace, product space, quotient space and inverse limit space 67
8. Connectedness 73
Exercise II 76
CHAPTER III. VARIOUS TOPOLOGICAL SPACES 80
1. T1, T2, regular and completely regular spaces 80
2. Normal space and fully normal space 83
3. Compact space and paracompact space 94
4. Axioms of countability 100
5. Metric space 104
Exercise III 114
CHAPTER IV. COMPACT SPACES AND RELATED TOPICS 117
1. Product of compact spaces 117
2. Compactification 126
3. Compact space and the lattice of continuous functions 143
4. Extensions of the concept of compactness 150
Exercise IV 158
CHAPTER V. PARACOMPACT SPACES AND RELATED TOPICS 160
1. Fundamental theorem 160
2. Further properties of paracompact spaces 165
3. Countably paracompact space 175
4. Modifications of the concept of paracompactness 181
5. Characterization by product spaces 185
Exercise V 193
CHAPTER VI. METRIZABLE SPACES AND RELATED TOPICS 195
1. Metrlzability 195
2. Imbedding 219
3. Union and image of metrizable spaces 224
4. Uniform space 232
5. Proximity space 251
6. P-spaces 263
Exercise VI 281
CHAPTER VII. TOPICS RELATED TO MAPPINGS 284
1. Mapping space 284
2. Metric space, paracompact space and continuous mapping 301
3. Theory of inverse limit space 316
4. Theory of selection 328
Exercise VII 350
EPILOGUE 353
BIBLIOGRAPHY 355
INDEX 371

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 1-4832-7816-6 / 1483278166
• ISBN-13: 978-1-4832-7816-2 / 9781483278162