Convergence Classes of L-Filters in L,M-Fuzzy Topological Spaces

Abstract

An L,M-fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L-filter (of crisp degree) on X to be convergent to a molecule in LX. By means of L,M-fuzzy topological neighborhood operators, we show that the category of L,M-fuzzy topological convergence spaces is isomorphic to the category of L,M-fuzzy topological spaces. Moreover, two characterizations of L-topological spaces are presented and the relationship with other convergence spaces is concretely constructed.