Characterization of convergence in fuzzy topological spaces

Abstract

ABSTRACT. In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,i]

Net-theoretical convergence in (L,M)-fuzzy cotopological spaces

“…There are lots of papers [4][5][6]8,9,18,19,26] that focus on fuzzy convergence theory based on fuzzy filters. In [18], Lowen considered prefilters (which are filters in the lattice [0, 1] X ) in the theory of convergence in fuzzy topological spaces.…”

“…In [18], Lowen considered prefilters (which are filters in the lattice [0, 1] X ) in the theory of convergence in fuzzy topological spaces. Further Lowen and Lowen [19] gave a necessary and sufficient condition for convergence functions to be induced by fuzzy topologies. Later on, Jäger [8] introduced stratified L-fuzzy convergence spaces and showed that the category of stratified L-topological spaces can be embedded in the category of stratified L-fuzzy convergence spaces as a reflective subcategory.…”

On convergence theory in fuzzy topological spaces and its applications

“…In 1979 Lowen [20] introduced and studied the theory of convergence for fuzzy filters (prefilters) in fuzzy topological spaces and applied the results to describe fuzzy compactness and fuzzy continuity. This was followed by an extensive study of the convergence theory of fuzzy filters in fuzzy topological spaces by several authors [7], [9]- [12], [21], [22], [26], [27], [31] from different standpoints. However, the concepts of Q-relation and Q-neighborhood of fuzzy points have not been used in these approaches.…”

“…In 1980 Pu and Liu [28], by means of the concept of a Q-neighborhood of a fuzzy point in a fuzzy topological space, gave the notion of convergence for fuzzy nets. The relationship between the two types of convergence was studied by Lowen in [21]. This was also followed by an extensive study of the convergence theory in fuzzy topological spaces by several authors [7], [8], [13], [21]- [24], [28]- [30] from different standpoints.…”

“…The relationship between the two types of convergence was studied by Lowen in [21]. This was also followed by an extensive study of the convergence theory in fuzzy topological spaces by several authors [7], [8], [13], [21]- [24], [28]- [30] from different standpoints. In this paper, we will give new concepts of convergence and adherence for fuzzy filters (prefilters in the sense of Lowen [20]) and fuzzy nets in fuzzy topological spaces.…”