An equivalent condition for a uniform space to be coverable (Q1004042)

The classical theory of covering spaces deals with spaces with nice properties such as ``semi-locally simply connected''. There is a considerable literature devoted to defining universal covers for spaces which are locally bad. A general reference might be \textit{V. Berestovskii} and \textit{C. Plaut} [Topology Appl. 154, No.~8, 1748--1777 (2007; Zbl 1116.54016)]. The author studies uniform spaces which are coverable in the sense that there is a nice basis for the uniformity. There is a characterization of the chain connected uniform spaces which are coverable. In addition, the author provides two (sophisticated) examples. Details are much too complex to be described here.