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$\mathbf{dfGDitop}$ is topological over $\mathbf{dfTex}\times\mathbf{dfTex}$. By means of spectrum idea, (di)compactness in graded ditological texturespaces is defined as a generalization of (di)compactness in ditopological case and its relation with the ditopological case is investigated. Moreover, using graded difilters, two characterizations of dicompactness of graded ditological texture spaces are obtained.