| 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:
|
http://hdl.handle.net/10338.dmlcz/118970 |
| . |
| 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 Unif.to 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 |
| . |
