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Title: On the quantification of uniform properties (English)
Author: Lowen, R.
Author: Windels, B.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 38
Issue: 4
Year: 1997
Pages: 749-759
Category: math
Summary: Approach spaces ([4], [5]) turned out to be a natural setting for the quantification of topological properties. Thus a measure of compactness for approach spaces generalizing the well-known Kuratowski measure of non-compactness for metric spaces was defined ([3]). This article shows that approach uniformities (introduced in [6]) have the same advantage with respect to uniform concepts: they allow a nice quantification of uniform properties, such as total boundedness and completeness. (English)
Keyword: uniform space
Keyword: approach uniform space
Keyword: totally bounded
Keyword: precompact
Keyword: complete
Keyword: measure of total boundedness
Keyword: measure of completeness
MSC: 54B30
MSC: 54E15
MSC: 54E35
idZBL: Zbl 0980.54020
idMR: MR1603710
Date available: 2009-01-08T18:37:44Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Čech E.: Topological Spaces.Interscience Publishers, 1966. MR 0211373
Reference: [2] Kuratowski C.: Sur les espaces complets.Fund. Math. 15 (1930), 301-309.
Reference: [3] Lowen R.: Kuratowski's measure of non-compactness revisited.Quarterly J. Math. Oxford 39 (1988), 235-254. Zbl 0672.54025, MR 0947504
Reference: [4] Lowen R.: Approach spaces: a common supercategory of TOP and MET.Math. Nachrichten 141 (1989), 183-226. Zbl 0676.54012, MR 1014427
Reference: [5] Lowen R.: Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad.Oxford Mathematical Monographs, Oxford University Press, 1997. Zbl 0891.54001, MR 1472024
Reference: [6] Lowen R., Windels B.: AUnif, a common supercategory of pMET and appear in Int. J. Math. Math. Sci. Zbl 0890.54024, MR 1486952
Reference: [7] Lowen R., Windels B.: Quantifying completion.submitted for publication. Zbl 0962.54023
Reference: [8] Preuss G.: Theory of Topological Structures.Kluwer Academic Publishers, 1987. Zbl 0649.54001, MR 0937052
Reference: [9] Willard S.: General Topology.Addison Wesley Publishing Company, 1970. Zbl 1052.54001, MR 0264581


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