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Encyclopaedia of Mathematical Sciences Ser.: General Topology III : Paracompactness, Function Spaces, Descriptive Theory by G. G. Gould (1995, Hardcover)

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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.

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
3540546987
ISBN-13
9783540546986
eBay Product ID (ePID)
2810148

Product Key Features

Author
G. G. Gould
Publication Name
General Topology III : Paracompactness, Function Spaces, Descriptive Theory
Format
Hardcover
Language
English
Series
Encyclopaedia of Mathematical Sciences Ser.
Publication Year
1995
Type
Textbook
Number of Pages
VIII, 232 Pages

Dimensions

Item Length
9.3in
Item Width
6.1in
Item Weight
40.6 Oz

Additional Product Features

Series Volume Number
51
Number of Volumes
1 Vol.
Lc Classification Number
Qa611-614.97
Table of Content
I. Paracompactness and Metrization. The Method of Covers in the Classification of Spaces.- II. Spaces of Mappings and Rings of Continuous Functions.- III. Descriptive Set Theory and Topology.- Author Index.
Copyright Date
1995
Topic
Geometry / General, Topology, Logic
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Mathematics

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Encyclopaedia of Mathematical Sciences Ser.: General Topology III : Paracompactness, Function Spaces, Descriptive Theory by G. G. Gould (1995, Hardcover)

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