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

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.

More on closed non-vanishing ideals in CB(X)

Let X be a completely regular topological space. For each closed non-vanishing ideal H of CB(X), the normed algebra of all bounded continuous scalar-valued mappings on X equipped with pointwise addition and multiplication and the supremum norm, we study its spectrum, denoted by 𝔰𝔭(H). We make a correspondence between algebraic properties of H and topological properties of 𝔰𝔭(H). This continues some previous studies, in which topological properties of 𝔰𝔭(H) such as the Lindelöf property, paracompactness, σ-compactness and countable compactness have been made into correspondence with algebraic properties of H. We study here other compactness properties of 𝔰𝔭(H) such as weak paracompactness, sequential compactness and pseudocompactness. We also study the ideal isomorphisms between two non-vanishing closed ideals of CB(X).

On Slight Omega Continuity and Irresoluteness between Generalized Topological Spaces

We introduce slightly ω - ( μ 1 , μ 2 ) -continuous and slightly ω - ( μ 1 , μ 2 ) -irresolute functions as two new classes of functions on generalized topological spaces. We obtained several properties and characterizations of these functions. Moreover, we deal with preservations of Lindelofness, mild Lindelofness, mildly countable compactness, and connectedness under images or inverse images of a class of functions, which gives symmetric relationships.

Leray–Schauder Alternatives for Maps Satisfying Countable Compactness Conditions

In this paper we present Leray–Schauder alternatives for a general class of Mönch type maps.

Approximation in quantum measure spaces

The objective of the present paper is to introduced and study the notion of μ-approximation by a subfamily K of a difference poset E. Various properties are proved and then applied to obtain some crucial results including a generalization of the Marczewski Theorem which states that countable compactness is sufficient for σ-additivity of a supermodular measure μ.