THE m-CONVERGENCE THEORY IN FUZZY TOPOLOGICAL SPACES

Abstract

In this paper, the m-convergences of fuzzy nets and fuzzy filters are introduced in a fuzzy topological space. The relations between m-convergences of fuzzy nets and fuzzy filters are investigated as are the relations between Hausdorff fuzzy topology and m-convergences of fuzzy nets and fuzzy filters. Characterizations of Hausdorff fuzzy topology in terms of neighborhoods and quasi-coincident neighborhoods and of minimal Hausdorff fuzzy topology in terms of m-convergence of fuzzy filters, are established. We study the relations between m-convergence of fuzzy nets and m-compactness, and between minimal Hausdorff fuzzy topology and m-compactness in a fuzzy topological space.

Mathematics Subject Classification (2000): 54A40.
Quaestiones Mathematicae 28(2005), 123–135.