UID:
almahu_9947367745502882
Format:
1 online resource (761 p.)
ISBN:
1-281-71607-3
,
9786611716073
,
0-08-087988-8
Series Statement:
North-Holland mathematical library ; 41
Content:
Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.
Note:
Description based upon print version of record.
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Front Cover; Topics in General Topology; Copyright Page; Contents; Preface; Chapter 1. Extensions of Mappings I; Introduction; 1. Generalized uniform spaces and semi-uniform spaces; 2. Completeness, completions and extensions of spaces; 3. Extensions of continuous maps from dense subspaces; Appendix. A generalization of the Ascoli Theorem; References; Chapter 2. Extensions of Mappings II; Introduction; 1. Preliminaries; 2. C*-, C-, Pm- and P-embeddings; 3. Unions of C*-embedded subsets; 4. C*-embedding in product spaces; 5. Homotopy extension property; References
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Chapter 3. Normality of Product Spaces IIntroduction; 1. Fundamental results; 2. The first of Morita's three conjectures; 3. The second and third of Morita's three conjectures; References; Chapter 4. Normality of Product Spaces II; 1. Products of normal spaces with metric spaces; 2. Products of normal spaces with generalized metric spaces; References; Chapter 5. Generalized Paracompactness; Introduction; 1. Preliminaries; 2. Characterizations of paracompactness; 3. Characterizations of submetacompactness; 4. Characterizations of metacompactness; 5. Characterizations of subparacompactness
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1. Metrizability in terms of g-functions2. Metrizability in terms of base of point-finite rank; 3. Metrizability in terms of hereditary property; 4. Some other aspects; References; Chapter 8. Metrization II; Iritroduction; 1. Spaces which contain a copy of S? or S2; 2. Spaces dominated by metric subsets; 3. Spaces with s-hereditarily closure-preserving k-networks; 4. Spaces with certain point-countable covers; 5. Quotient s-images of locally separable metric spaces; 6. ?-Metrizable spaces and d-metrizable spaces; References; Chapter 9. Generalized Metric Spaces I; Introduction
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1. Lašnev space and N-space2. Developable space; 3. M-space and related topics; 4. Universal spaces; References; Chapter 10. Generalized Metric Spaces II; Introduction; 1. Review of basic results; 2. Closure-preserving collections and definitions of various stratifiable spaces; 3. Expandability, extension property, and sup-characterization of stratifiable spaces; 4. Classes of M1-spaces; 5. Embeddings; 6. Closed maps and perfect maps; 7. Related topics; 8. Problems; References; Chapter 11. Function Spaces; 1. Introduction and notation; 2. Some properties of Cn*(X); 3. Some properties of Ck(X)
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4. Some properties of Cp(X)
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English
Additional Edition:
ISBN 0-444-70455-8
Language:
English
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