The \(L \omega\)-compactness in \(L \omega\)-spaces (Q2319274)

Summary: The concepts of \(\alpha \omega\)-remote neighborhood family, \(\gamma \omega\)-cover, and \(L \omega\)-compactness are defined in \(L \omega\)-spaces. The characterizations of \(L \omega\)-compactness are systematically discussed. Some important properties of \(L \omega\)-compactness such as \(\omega\)-closed heredity, arbitrarily multiplicative property, and preserving invariance under \(\omega\)-continuous mappings are obtained. Finally, the Alexander \(\omega\)-subbase lemma and the Tychonoff product theorem with respect to \(L \omega\)-compactness are given.