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A metrizable completely regular ordered space

Hans-Peter A. KünziStephen W. Watson — 1994

Commentationes Mathematicae Universitatis Carolinae

We construct a completely regular ordered space ( X , 𝒯 , ) such that X is an I -space, the topology 𝒯 of X is metrizable and the bitopological space ( X , 𝒯 , 𝒯 ) is pairwise regular, but not pairwise completely regular. (Here 𝒯 denotes the upper topology and 𝒯 the lower topology of X .)

On uniformly locally compact quasi-uniform hyperspaces

Hans-Peter A. KünziSalvador RomagueraM. A. Sánchez-Granero — 2004

Czechoslovak Mathematical Journal

We characterize those Tychonoff quasi-uniform spaces ( X , 𝒰 ) for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family 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 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...

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