On 1-sequence-covering Pi-s-images of Locally Separable Metric Spaces

Nguyen Van Dung

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 n-network consisting of cosmic
spaces (sn-second countable spaces, $\aleph_0$-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].

Keywords

1-sequence-covering, $\sigma$-strong $sn$-network,

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