A Tychonoff theorem for graded ditopological texture spaces

Abstract

In this paper, initial and product graded ditopologies are formulated and accordingly it is shown that dfGDitop is a topological structure over dfTex dfTex. By means of spectrum idea, (di)compactness in graded ditological texture spaces is defined as a generalization of (di)compactness in ditopological case and its relation with the ditopological case is investigated. Moreover, the relations between graded difilters and dicompactness of graded ditological texture spaces are studied.