t-prefilter theory

Filter Convergence and Fuzzy Topology

“…The conditions (P4) and (P5) follow from Theorem 3.7 and Proposition 3.5 [8], respectively. [13] showed that a fuzzy topological space (X, δ) is ultrafilter α-compact for Convergence (VI) iff it is strong fuzzy compact. In [2], the Tychonoff theorems for α-compactness and strong compactness, respectively, were proved using the Alexander Subbase Theorem.…”

“…Now, we introduce a characterization of an ultra tprefilter Definition 4.10. [13] A α-prefilter F on X is called an ultra α-prefilter (=maximal α-prefilter) if there is no strictly finer α-prefilter than F. Definition 4.11. [13] Let F be α-prefilter on X.…”

“…[13] A α-prefilter F on X is called an ultra α-prefilter (=maximal α-prefilter) if there is no strictly finer α-prefilter than F. Definition 4.11. [13] Let F be α-prefilter on X. We say that a subset T of X is α-included in F if every fuzzy set A in X with A −1 (α, 1] = T is an element of F.…”

Uniform-type structures on lattice-valued spaces and frames

“…There the authors show that levels and level topologies may be interpreted as a system of frame homomorphisms satisfying some categorical conditions. Indeed, L-fuzzy and traditional structures, can be related via the functor L and its levels { : ∈ L} (see, among others [19,[35][36][37]18] for topologies and [20,24,9,10] for filters and uniformities). Two relevant facts of the level (topological) functors { | ∈ L} are:…”

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.…”