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 texture
spaces 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.

Keywords

• Dicompactness spectrum,product graded ditopology,initial graded ditopology,compactness,cocompactness

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