Ditopological texture spaces and intuitionistic sets

Abstract

In this paper it is shown that the lattice of intuitionistic subsets of a set X in the sense of D. Çoker may be represented as a special type of texture space, called an intuitionistic texture on X, and various characterizations are given. It is established that intuitionistic topologies are mapped to ditopologies on the corresponding texture, and some notions of compactness and stability are considered.