Dieudonné complete bispaces (Q2754984)

A bispace is a triple \((X,P,Q)\), where \(X\) is a set and \(P\), \(Q\) are topologies on \(X\). Such a triple is called Dieudonné complete if it admits a quasi-uniformity \(U\) for which \(P\) is induced by \(U\), \(Q\) is induced by the conjugate of \(U\), and which is bicomplete. In this paper pairwise Tikhonov Dieudonné complete bispaces are characterized in terms of the canonical bitopological compactification, and from this a characterization of those \(T_0\) spaces that admit a bicomplete quasi-uniformity. These characterizations are given in terms of bispaces which are 2-perfect pre-images of bicompletely quasi-metrizable bispaces, which, in turn, are characterized in terms of the notion of an \(M\)-bispace. Further comparisons are made with the analogous metric topological theorems.