On uniformly locally compact quasi-uniform hyperspaces
We characterize those Tychonoff quasi-uniform spaces (X, U) for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family K0(X) of nonempty compact subsets of X. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-un...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
2017
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| Online Access: | http://hdl.handle.net/10835/4864 |
| _version_ | 1789406601973596160 |
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| author | Künzi, H. P. A Romaguera, S. Sánchez-Granero, M.A |
| author_facet | Künzi, H. P. A Romaguera, S. Sánchez-Granero, M.A |
| author_sort | Künzi, H. P. A |
| collection | DSpace |
| description | We characterize those Tychonoff quasi-uniform spaces (X, U) for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family K0(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 K0(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 σ-compact if and only if its (lower)
semicontinuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces (X, U) for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on K0(X) is obtained. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-4864 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-48642023-04-12T19:38:43Z On uniformly locally compact quasi-uniform hyperspaces Künzi, H. P. A Romaguera, S. Sánchez-Granero, M.A We characterize those Tychonoff quasi-uniform spaces (X, U) for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family K0(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 K0(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 σ-compact if and only if its (lower) semicontinuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces (X, U) for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on K0(X) is obtained. 2017-06-16T08:26:11Z 2017-06-16T08:26:11Z 2004 info:eu-repo/semantics/article http://hdl.handle.net/10835/4864 en http://www.dml.cz/handle/10338.dmlcz/127878 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess The original publication is available at www.dml.cz |
| spellingShingle | Künzi, H. P. A Romaguera, S. Sánchez-Granero, M.A On uniformly locally compact quasi-uniform hyperspaces |
| title | On uniformly locally compact quasi-uniform hyperspaces |
| title_full | On uniformly locally compact quasi-uniform hyperspaces |
| title_fullStr | On uniformly locally compact quasi-uniform hyperspaces |
| title_full_unstemmed | On uniformly locally compact quasi-uniform hyperspaces |
| title_short | On uniformly locally compact quasi-uniform hyperspaces |
| title_sort | on uniformly locally compact quasi-uniform hyperspaces |
| url | http://hdl.handle.net/10835/4864 |
| work_keys_str_mv | AT kunzihpa onuniformlylocallycompactquasiuniformhyperspaces AT romagueras onuniformlylocallycompactquasiuniformhyperspaces AT sanchezgraneroma onuniformlylocallycompactquasiuniformhyperspaces |