On half-completion and bicompletion of quasi-metric spaces

Abstract

summary:We characterize the quasi-metric spaces which have a quasi-metric half-comp\-le\-tion 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.