MATHEMATICA BOHEMICA, Vol. 131, No. 1, pp. 15-28, 2006

# A new form of fuzzy $\alpha$-compactness

## Fu-Gui Shi

Fu-Gui Shi, Beijing Institute of Technology, Department of Mathematics, Beijing 100081, P.R. China, e-mail: fuguishi@bit.edu.cn or f.g.shi@263.net

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 $\alpha$-Lindelof property are also researched.

Keywords: $L$-topology, compactness, $\alpha$-compactness, countable $\alpha$-compactness, $\alpha$-Lindelof property, $\alpha$-irresolute map, $\alpha$-continuous map

Classification (MSC 2000): 54A40, 54D35

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