A NEW NOTION OF FUZZY PS-COMPACTNESS

Abstract

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity. It is known that compactness and its stronger and weaker forms play very im- portant roles in topology. Based on fuzzy topological spaces introduced by Chang (4), various kinds of fuzzy compactness (2-4,7,11) have been established. However, these concepts of fuzzy compactness rely on the structure of L and L is required to be completely distributive. In (10), for a complete De Morgan algebra L, Shi in- troduced a new definition of fuzzy compactness in L-topological spaces using open L-sets and their inequality. This new definition doesn't depend on the structure of L. In this paper, following the lines of (10), we introduce a new notion of PS- compactness in L-topological spaces by means of pre-semi-open L-sets and their inequality. This notion can also be characterized by pre-semi-closed L-sets and their inequality and is a strong form of semi-compactness(9). This form of PS- compactness is a good generalization and has many characterizations when L is completely distributive De Morgan algebra. 2. Preliminaries