Stone -Cech compactifications of ditopological texture spaces

Abstract

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, Ø and for which arbitrary meet coincides with intersection and finite joins coincide with union. Then (S, S) is called a texture space. In this paper, a suitable evaluation difunction is defined and an approach for the construction of the Stone- Cech compactification of ditopological texture spaces is given. It is also shown that the Stone- Cech compactification of a topological space can be obtained using highly economic structure of the unit texture.

Keywords: Texturing; texture space; ditopology; evaluation difunction; dicompactness; Tychonoff dicube

Quaestiones Mathematicae 32(2009), 15–33