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 |
| Summary: | 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. |
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