Relations between the good definitions of compactness in L-fuzzy topological spaces

Abstract In this paper we state the different definitions of compactness in L-fuzzy topological spaces where L is a completely distributive lattice. We obtain other characterizations of some of these notions and study them with respect to their goodness. Finally, we establish the inter-relations between the compactnesses which are good extensions. We also obtain an improvement of our Theorem 7.6 in [3].