L-Ponomarev system and images of locally separable metric spaces

Abstract

We introduce the notion of an L-Ponomarev system (f, M, X, P * n), and give characterizations of certain msss-images (resp., mssc-images) of locally separable metric spaces. As an application, we get a new characterization of quotient msss-images (mssc-images) of locally separable metric spaces, which is helpful in solving Velichko's question (1987). Recently, Dung gave some characterizations for certain msss-images (resp., mssc-images) of locally separable metric spaces in the class of regular and T 1-spaces (see in [3, 4]). This leads us to consider the following question.