$ls$-Ponomarev-systems and compact images of locally separable metric spaces

Abstract

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