Modern General Topology
- 2nd Edition - December 24, 2014
- Latest edition
- Author: Jun-Iti Nagata
- Editors: N. G. De Bruijn, J. De Groot, A. C. Zaanen
- Language: English
Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and… Read more
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.
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 IChapter 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 IIChapter III Various Topological Spaces 1. T1, Τ2, Regular and Completely Regular Spaces 2. Normal Space and Fully Normal Space 3. Compact Space and Paracompact Space 4. Axioms of Countability 5. Metric Space Exercise IIIChapter IV Compact Spaces and Related Topics 1. Product of Compact Spaces 2. Compactification 3. Compact Space and the Lattice of Continuous Functions 4. Extensions of the Concept of Compactness Exercise IVChapter V Paracompact Spaces and Related Topics 1. Fundamental Theorem 2. Further Properties of Paracompact Spaces 3. Countably Paracompact Space 4. Modifications of the Concept of Paracompactness 5. Characterization by Product Spaces Exercise VChapter VI Metrizable Spaces and Related Topics 1. Metrizability 2. Imbedding 3. Union and Image of Metrizable Spaces 4. Uniform Space 5. Proximity Space 6. P-Spaces Exercise VIChapter VII Topics Related to Mappings 1. Mapping Space 2. Metric Space, Paracompact Space and Continuous Mapping 3. Theory of Inverse Limit Space 4. Theory of Selection Exercise VIIEpilogueBibliographyIndex
- Edition: 2
- Latest edition
- Published: December 24, 2014
- Language: English
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