The Katětov construction modified for a T0T0-quasi-metric space

Abstract

We discuss the existence and uniqueness of a T0T0-quasi-metric space qUqU defined by the following three conditions: (i) qUqU is bicomplete and supseparable, (ii) every isometry between two finite subspaces of qUqU extends to an isometry of qUqU onto itself, and (iii) qUqU contains an isometric copy of every supseparable T0T0-quasi-metric space.