Lattice repleteness and some of its applications to topology

Abstract

We deal with the general concept of lattice repleteness. Specifically, we systematize the study of several important special cases of repleteness, namely, realcompactness, α-completeness, N-compactness, and Borel-completeness; we apply our general results on repleteness to specific lattices in topological spaces, in particular, to analytic spaces; we utilize the concept of G δ-closure to obtain necessary or sufficient conditions for repleteness (this portion of our work generalizes important theorems of Mrówka on Stone-Čechcompactification, of Frolik on realcompact spaces, and of Wenjen on realcompact spaces); finally, we extend the measure representation material of Varadarajan and then we utilize the results to obtain further applications to repleteness.