| Title:
|
On uniformly locally compact quasi-uniform hyperspaces (English) |
| Author:
|
Künzi, H. P. A. |
| Author:
|
Romaguera, S. |
| Author:
|
Sánchez-Granero, M. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
215-228 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize those Tychonoff quasi-uniform spaces $(X,\mathcal {U})$ for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family $\mathcal {K}_{0}(X)$ of nonempty compact subsets of $X$. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space $X$ is uniformly locally compact on $\mathcal {K}_{0}(X)$ if and only if $X$ is paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is $\sigma $-compact if and only if its (lower) semicontinuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces $(X,\mathcal {U})$ for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on $\mathcal {K}_{0}(X)$ is obtained. (English) |
| Keyword:
|
Hausdorff-Bourbaki quasi-uniformity |
| Keyword:
|
hyperspace |
| Keyword:
|
locally compact |
| Keyword:
|
cofinally complete |
| Keyword:
|
uniformly locally compact |
| Keyword:
|
co-uniformly locally compact |
| MSC:
|
54B20 |
| MSC:
|
54D45 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 1051.54023 |
| idMR:
|
MR2040233 |
| . |
| Date available:
|
2009-09-24T11:11:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127878 |
| . |
| Reference:
|
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