Measurement of Countable Compactness and Lindelöf Property in RL‐Fuzzy Topological Spaces

Abstract

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

Preopenness Degree in R L -Fuzzy Bitopological Spaces

“…Further investigations are conducted regarding the RL-fuzzy compactness in RL-fuzzy topological spaces. As a consequence of their work, Zhang et al [8] presented the Lindelöf property degree as well as the countable RLfuzzy compactness degree of an L-subset. It is clear that the gradation of fuzzy compactness and Lindelöf property in the sense of Kubiak and Šostak are special cases of the corresponding degrees in RL-fuzzy topology.…”

A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces

“…Some relevant properties of RL-fuzzy compactness in RL-fuzzy topological spaces are further investigated. Later on, Zhang et al [15] defined the degree of Lindelöf property and the degree of countable RL-fuzzy compactness of an L-fuzzy set, where L is a complete DeMorgan algebra. Since L-fuzzy topology in the sense of Kubiak and Šostak is a special case of RLfuzzy topology, the degree of RL-fuzzy compactness and the degree of Lindelöf property are extensions of the corresponding degrees in L-fuzzy topology.…”