A note on \(\aleph_0\) - spaces

Abstract

In this paper, we prove that a space is an \(\aleph_0\)- space if it is an \(\aleph_1\)-compact space with a \(\sigma\)-weakly hereditarily closure-preserving strong \(cs\)-network. As an application of this result, we prove that a space with a nontrivial convergent sequence is an \(\aleph_0\)-space if it has a \(\sigma\)-weakly hereditarily closure-preserving strong \(cs\)-network.