Special uniformities (Q1908579)

Some classes of those uniform spaces are studied, which have the Čech uniformity for its totally bounded modification (the classes are defined by means of properties of covers of cozero sets). Main results deal with completions of spaces \(X\) and their relations to \(\beta X\) and \(vX\). A typical result: Let, in a completely regular space \(X\), \({\mathcal U}\) be a collection of normal covers having a moderate special refinement; then the completion of \((X, {\mathcal U})\) is homeomorphic to \(vX\). (No references to many known related results are given).