A double completion for an arbitrary T0-quasi-metric space

We present a conjugate invariant method for completing any T0-quasi-metric space. The completion is built as an extension of the bicompletion of the original space. For balanced T0-quasi-metric spaces our completion yields up to isometry the completion due to Doitchinov. The question which uniformly continuous maps between T0-quasi-metric spaces can be extended to the constructed completions leads us to introduce and investigate a new class of maps, which we call balanced maps.