Degrees of compactness in (L, M)-fuzzy convergence spaces and its applications

Based on completely distributive lattices L and M, we define the degrees of compactness of (L, M)-fuzzy convergence spaces, (L, M)-fuzzy topological spaces, (L, M)-fuzzy pseudo-quasi-metric spaces and pointwise (L, M)-fuzzy quasi-uniform spaces. It is shown that (1) the Tychonoff Theorem with respect to the compactness degrees holds in (L, M)-fuzzy convergence spaces and (L, M)-fuzzy topological spaces; (2) the compactness degrees of an (L, M)-fuzzy pseudo-quasi-metric space and a pointwise (L, M)-fuzzy quasi-uniform space are equal to the compactness degrees of their induced (L, M)-fuzzy topological spaces, respectively; (3) an (L, M)-fuzzy pseudo-quasi-metric space can induce a pointwise (L, M)-fuzzy quasi-uniform space and their compactness degrees are equal. (C) 2014 Elsevier B.V. All rights reserved.