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General Topology III

Paracompactness, Function Spaces, Descriptive Theory

  • Book
  • © 1995

Overview

Editors:
  1. A. V. Arhangel’skii

    1. Department of Mathematics, University of Moscow, Moscow, Russia
      Department of Mathematics, Ohio University, Athens, USA

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Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 51)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-vii
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  2. Paracompactness and Metrization. The Method of Covers in the Classification of Spaces

    • A. V. Arhangel’skii
    Pages 1-70

  3. Spaces of Mappings and Rings of Continuous Functions

    • A. V. Arhangel’skii
    Pages 71-156

  4. Descriptive Set Theory and Topology

    • M. M. Choban
    Pages 157-219

  5. Back Matter

    Pages 221-232
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Keywords

About this book

The problem of metrization of topological spaces has had an enormous influence on the development of general topology. Singling out the basic topo­ logical components of metrizability has determined the main reference points in the construction of the classification of topological spaces. These are (pri­ marily) paracompactness, collectionwise normality, monotonic normality and perfect normality, the concepts of a stratifiable space, Moore space and u­ space, point-countable base, and uniform base. The method of covers has taken up a leading role in this classification. Of paramount significance in the applications of this method have been the properties of covers relating to the character of their elements (open covers, closed covers), the mutual dispo­ sition of these elements (star finite, point finite, locally finite covers, etc. ), as well as the relations of refinement between covers (simple refinement, refine­ ment with closure, combinatorial refinement, star and strong star refinement). On this basis a hierarchy of properties of paracompactness type has been sin­ gled out, together with the classes of spaces corresponding to them, the most important of which is the class of paracompacta. The behaviour of families of covers with respect to the topology of a space has important significance. Here, first and foremost, is the notion of a refining family of covers, a development which appears in several modifications and, together with the notion of paracompactness, plays a key role in metrization problems.

Editors and Affiliations

  • Department of Mathematics, University of Moscow, Moscow, Russia

    A. V. Arhangel’skii

  • Department of Mathematics, Ohio University, Athens, USA

    A. V. Arhangel’skii

About the editor

 

Bibliographic Information

  • Book Title: General Topology III

  • Book Subtitle: Paracompactness, Function Spaces, Descriptive Theory

  • Editors: A. V. Arhangel’skii

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-662-07413-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Hardcover ISBN: 978-3-540-54698-6Published: 18 September 1995

  • Softcover ISBN: 978-3-642-08123-1Published: 01 December 2010

  • eBook ISBN: 978-3-662-07413-8Published: 09 March 2013

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: VIII, 232

  • Additional Information: Original Russian edition published by VINITI, Moscow, 1989

  • Topics: Topology, Geometry, Mathematical Logic and Foundations, Analysis, Probability Theory and Stochastic Processes

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