On uniform spaces with a small base and \(K\)-analytic \(C_c(X)\) spaces (Q492234)

The main theorem of this paper deals with the following equivalence statement: We can find an admissible uniformity for a set \(X\) larger than or equal to the Nachbin uniformity with a \(\mathfrak{G}\)-base iff there exists a resolution on the space \(C_c(X)\) of all real-valued continuous functions defined on \(X\) with the compact-open topology consisting of equicontinuous sets. Then this result is applied to topological groups with small base generalizing some of the research of Grabriyelyan, Kakol and Leidermann to uniformities. Among them the interplay between the existence of certain topological groups \(G\) with a \(\mathfrak{G}\)-base and the \(K\)-analyticity or the existence of a resolution consisting of equicontinuous sets of the locally convex space \(C_c(G)\) is described. At the end of paper a number of consequences in order is given.