# On the quantification of uniform properties

Commentationes Mathematicae Universitatis Carolinae (1997)

- Volume: 38, Issue: 4, page 749-759
- ISSN: 0010-2628

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topLowen, Robert, and Windels, Bart. "On the quantification of uniform properties." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 749-759. <http://eudml.org/doc/22304>.

@article{Lowen1997,

abstract = {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.},

author = {Lowen, Robert, Windels, Bart},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {uniform space; approach uniform space; totally bounded; precompact; complete; measure of total boundedness; measure of completeness; Cauchy ideal},

language = {eng},

number = {4},

pages = {749-759},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On the quantification of uniform properties},

url = {http://eudml.org/doc/22304},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Lowen, Robert

AU - Windels, Bart

TI - On the quantification of uniform properties

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1997

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 38

IS - 4

SP - 749

EP - 759

AB - 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.

LA - eng

KW - uniform space; approach uniform space; totally bounded; precompact; complete; measure of total boundedness; measure of completeness; Cauchy ideal

UR - http://eudml.org/doc/22304

ER -

## References

top- Čech E., Topological Spaces, Interscience Publishers, 1966. Zbl0141.39401MR0211373
- Kuratowski C., Sur les espaces complets, Fund. Math. 15 (1930), 301-309. (1930) Zbl56.1124.04
- Lowen R., Kuratowski's measure of non-compactness revisited, Quarterly J. Math. Oxford 39 (1988), 235-254. (1988) Zbl0672.54025MR0947504
- Lowen R., Approach spaces: a common supercategory of TOP and MET, Math. Nachrichten 141 (1989), 183-226. (1989) Zbl0676.54012MR1014427
- Lowen R., Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press, 1997. Zbl0891.54001MR1472024
- Lowen R., Windels B., AUnif, a common supercategory of pMET and Unif, to appear in Int. J. Math. Math. Sci. Zbl0890.54024MR1486952
- Lowen R., Windels B., Quantifying completion, submitted for publication. Zbl0962.54023
- Preuss G., Theory of Topological Structures, Kluwer Academic Publishers, 1987. Zbl0649.54001MR0937052
- Willard S., General Topology, Addison Wesley Publishing Company, 1970. Zbl1052.54001MR0264581

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