On Uniformly Locally Compact Quasi-Uniform Hyperspaces.

Autor:	H. P. A. Künzi, S. Romaguera, M. A. Sánchez-Granero
Předmět:	HYPERSPACE FOUNDATIONS of geometry DIFFERENTIAL geometry NON-Euclidean geometry MATHEMATICS
Zdroj:	Czechoslovak Mathematical Journal; Mar2004, Vol. 54 Issue 1, p215-228, 14p
Abstrakt:	We characterize those Tychonoff quasi-uniform spaces (X, \maths/math> for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family {\mathscr{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 {\mathscr{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 σ-compact if and only if its (lower) semi-continuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces (X, \maths/math> for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on {\mathscr{K}_0}(X) is obtained. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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