Compactness in L-fuzzy topological spaces

Abstract

The aim of this paper is to introduce a new notion of L-fuzzy compactness in L-fuzzy topological spaces, which is a generalization of Lowen's fuzzy compactness in L-topological spaces. The union of two L-fuzzy compact L-sets is L-fuzzy compact. The intersection of an L-fuzzy compact L-set G and an L-set H with T*(H) = T is L-fuzzy compact. The L-fuzzy continuous image of an L-fuzzy compact L-set is L-fuzzy compact. The Tychonoff Theorem for L-fuzzy compactness is true.