Modern General Topology – Jun-Iti Nagata – 2nd Revised Edition


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.

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  • 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, ?2, 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 III

    Chapter 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 IV

    Chapter 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 V

    Chapter 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 VI

    Chapter 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 VII

  • Citation
    • Full Title: Modern General Topology
    • Author/s:
    • ISBN-10: 1483249972
    • ISBN-13: 9781483249971
    • Edition: 2nd Revised Edition
    • Publication date: 2014
    • Topic: Math
    • Subtopic: Topology
    • File Type: eBook
    • Idioma: English

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