L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic

Abstract

In the present paper we introduce and studywhere L is a complete residuated lattice. Sometimes we need more conditions on L such as the completely distributive law or that the "∧" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results (see [1,2]) are generalized and new consequences are obtained.