ls-Ponomarev-systems and compact images of locally separable metric spaces - Tran Van An; Nguyen Van Dung (Methods of Functional Analysis and Topology, 2009)
We introduce the notion of an ls-Ponomarev-system (f, M, X, {P_λ,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.