Published 2006-01-15
DOI:
https://doi.org/10.71712/Keywords
- strong cs-network,
- weakly hereditarily closure-preserving family,
- sequential space,
- \(\aleph_0\) - spaces
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How to Cite
Ge, Y. (2006). A note on \(\aleph_0\) - spaces. Scientia Series A: Mathematical Sciences, 12, 1-4. https://doi.org/10.71712/
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.
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