On \(\aleph_0\)-\(sn\)-networks

Abstract

In this paper, we discuss spaces with \(\aleph_0\)-\(sn\)-networks  and give some characterizations of \(\aleph_0\)-\(sn\)-metric spaces. For a space \(X\) we prove that \(X\) has a point-countable \(\aleph_0\)-\(sn\)-network if and only if \(X\) is an sequentially quotient, countable-to-one image of a metric space. and \(X\) is an \(\aleph_0\)-\(sn\)-metric space if and only if \(X\) is a sequentially quotient, \(\sigma\), countable-to-one image of a metric space