On ls-Ponomarev systems and s-images of locally separable metric spaces

Abstract

We introduce the notion of an ls-Ponomarev system (f,M,X, \( \{ \mathcal{P}_\lambda \} \)), and use this notion to give the necessary and sufficient conditions such that the mapping f is an s-mapping (a compact-covering mapping, a sequence-coveringmapping, a pseudo-sequence-covering mapping, a sequentially quotient mapping) from a locally separable metric space M onto a space X. As applications of these results, we systematically get the internal characterizations of certain s-images of locally separable metric spaces.