The bicompletion of the Hausdorff quasi-uniformity

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.