The bicompletion of the Hausdorff quasi-uniformity

2008/09/29 by Hans-Peter A. Kunzi, Hans-Peter A. Künzi, S. Romaguera +6
Mathematics · #54E15 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #math.GN #msc:54E15

paper · pdf · doi:10.48550/arxiv.0809.4964

arxiv created 2008/09/29 · openalex publication_date 2008/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conditions under which the Hausdorff quasi-uniformity \mathcal U_H of a quasi-uniform space (X,\mathcal U) on the set \mathcal P₀(X) of the nonempty subsets of X is bicomplete. Indeed we present an explicit method to construct the bicompletion of the T₀-quotient of the Hausdorff quasi-uniformity of a quasi-uniform space. It is used to find a characterization of those quasi-uniform T₀-spaces (X,\mathcal U) for which the Hausdorff quasi-uniformity \widetilde\mathcal U_H of their bicompletion (\widetildeX,\widetilde\mathcal U) on \mathcal P₀(\widetildeX) is bicomplete.

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