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The bicompletion of the Hausdorff quasi-uniformity |
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| Authors: | Hans-Peter A Künzi S Romaguera |
| Institution: | a Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa b Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain c Area of Geometry and Topology, Faculty of Science, Universidad de Almería, Spain |
| Abstract: | We study conditions under which the Hausdorff quasi-uniformity UH of a quasi-uniform space (X,U) on the set 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,U) for which the Hausdorff quasi-uniformity  of their bicompletion  on  is bicomplete. |
| Keywords: | 54E15 54B20 54D35 54E55 |
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