UID:
almahu_9947367848002882
Format:
1 online resource (533 p.)
Edition:
3rd ed.
ISBN:
1-282-03475-8
,
9786612034756
,
0-08-093379-3
Series Statement:
North-Holland mathematical library ; v. 33
Content:
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 ordere
Note:
Includes index.
,
Front Cover; Modern General Topology; Copyright Page; Contents; Chapter I. Introduction; 1. Set; 2. Cardinal numbers; 3. Ordinal numbers; 4. Zermelo's theorem and Zorn's lemma; 5. Topology of Euclidean plane; Exercise I; Chapter II. Basic Concepts in Topological Spaces; 1. Topological space; 2. Open basis and neighborhood basis; 3. Closure; 4. Convergence; 5. Covering; 6. Mapping; 7. Subspace, product space, quotient space and inverse limit space; 8. Connectedness; Exercise II; Chapter III. Various Topological Spaces; 1. T1, T2, regular and completely regular spaces
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2. Normal space and fully normal space3. Compact space and paracompact space; 4. Axioms of countability; 5. Metric space; Exercise IIII; Chapter IV. Compact Spaces and Related Topics; 1. Product of compact spaces; 2. Compactification; 3. More of compactifications; 4. Compact space and the lattice of continuous functions; 5. Extensions of the concept of compactness; 6. Realcompact space; Exercise IV; Chapter V. Paracompact Spaces and Related Topics; 1. Fundamental theorem; 2. Further properties of paracompact spaces; 3. Countably paracompact space and collectionwise normal space
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4. Modifications of the concept of paracompactness5. Characterization by product spaces; Exercise V; Chapter VI. Metrizable Spaces and Related Topics; 1. Metrizability; 2. Complete metrizability; 3. Imbedding; 4. Union and image of metrizable spaces; 5. Uniform space; 6. Proximity space; 7. P-space; 8. Various generalized metric spaces; Exercise VI; Chapter VII. Topics Related to Mappings; 1. Mapping space; 2. Metric space, paracompact space and continuous mapping; 3. Metrization of M-spaces; 4. Theory of inverse limit space; 5. Theory of selection; 6. More of extension theory
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7. Characterization of topological properties in terms of C(X)Exercise VII; Chapter VIII. Other Aspects; 1. Linearly ordered space; 2. Cardinal functions; 3. Dyadic space; 4. Measure and topological space; Exercise VIII; Epilogue; Bibliography; Index
Additional Edition:
ISBN 0-444-87655-3
Language:
English
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