Abstract:We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space $X$ is quasi-metric if and only if $X$ is finite.
Keywords: quasi-metric, quasi-uniform, half-completion, bicompletion, uniformly \newline weakly regular
AMS Subject Classification: 54E50, 54E35, 54E15