form the base of a topology on the Stone spectrum Q(R) such that Q(R) becomes a zero-dimensional, completely regular Hausdorff space. The sets QP (R) are closed-open. If the von Neumann algebra R is abelian, then the Stone spectrum Q(R) is homeomorphic to the Gelfand spectrum Ω(R) of R. For an arbitrary non-abelian unital von Neumann algebra R, the Stone spectrum can hence be regarded as a non-...

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fu...

This paper is aimed at constructing a topology on fuzzy hypersoft sets. The concepts of topology, open(closed) sets, interior, closure, base and subspace are also introduced here some important theorems have been established.

The purpose of this paper is to introduce and investigate the concept of fuzzy almost r-minimal continuous function between fuzzy minimal spaces and fuzzy topological spaces. Particularly, we investigate characterizations for the fuzzy almost r-minimal continuity by using generalized fuzzy r-open sets.

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

In this paper, the notion of βS∗−compactness is introduced in L−fuzzy topological spaces based on S∗−compactness. A βS∗−compactness L-fuzzy set is S∗−compactness and also β−compactness. Some of its properties are discussed. We give some characterizations of βS∗−compactness in terms of pre-open, regular open and semi-open L−fuzzy set. It is proved that βS∗−compactness is a good extension of β−co...

We show that the family Sem = mREG = mCF of regular multiset languages is closed under applications of finite and iterated multiset-union, finite and iterated multiset-intersection, and multiset-subtraction. For the class Sem(šk) of semilinear subsets of šk, or that of Žk, Sem := ⋃k≥0 Sem(Žk), this amounts to verify, that the component-wise maximum, minimum or non-negative subtraction of pairs ...