Document Type : Research Paper


Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China


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


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