A Wallman-type compactification of texture spaces

A texturing on a set S is a point separating, complete, completely distributive lattice S of subsets of S with respect to inclusion which contains S, ∅ and, for which arbitrary meet coincides with intersection and finite joins coincide with union. The pair (S, S) is known as a texture space. In this paper, the authors present the concept of embedding for texture spaces and define the notion of difilter on a texture space. Then a Wallman-type compactification is discussed for a class of ditopological texture spaces in terms of so-called difunctions introduced by Brown and his team and it is expressed in the class of molecular weakly bi-R₁ Hutton spaces.