The bicompletion of the Hausdorff quasi-uniformity
نویسنده
چکیده
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 T0spaces (X,U) for which the Hausdorff quasi-uniformity ŨH of their bicompletion (X̃, Ũ) on P0(X̃) is bicomplete.
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