The Lω-Compactness in Lω-Spaces

Abstract

The concepts of αω-remote neighborhood family, γω-cover, and Lω-compactness are defined in Lω-spaces. The characterizations of Lω-compactness are systematically discussed. Some important properties of Lω-compactness such as ω-closed heredity, arbitrarily multiplicative property, and preserving invariance under ω-continuous mappings are obtained. Finally, the Alexander ω-subbase lemma and the Tychonoff product theorem with respect to Lω-compactness are given.