On 1-sequence-covering $pi$-s-images of locally separable metric spaces

Abstract

In this paper, we give a characterization on 1-sequence-covering $pi$-s-images of locally separable metric spaces by means of point-countable $sigma$-strong sn-network consisting of cosmic spaces (sn-second countable spaces, $aleph_o$-spaces). As an application, we get a new characterization on 1-sequence-covering, quotient $pi$-s-images of locally separable metric spaces, which is helpful in solving Y. Tanaka and S. Xia’s question in [21].