COUNTABLE COMPACTNESS AND THE LINDEL¨OF PROPERTY OF L-FUZZY SETS

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. Many characterizations of countable compactnessand the Lindel¨of property are presented by means of open L-sets and closedL-sets when L is a completely distributive de Morgan algebra.

Keywords:

L-topology , Fuzzy Compactness , Countable Compactness , Lindel¨of Property