A new form of fuzzy $\alpha $-compactness

Abstract

A new form of $\alpha $-compactness is introduced in $L$-topological spaces by $\alpha $-open $L$-sets and their inequality where $L$ is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice $L$. It can also be characterized by means of $\alpha $-closed $L$-sets and their inequality. When $L$ is a completely distributive de Morgan algebra, its many characterizations are presented and the relations between it and the other types of compactness are discussed. Countable $\alpha $-compactness and the $\alpha $-Lindelöf property are also researched.