A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

in this paper, a certain new connectedness of l-fuzzy subsets inl-topological spaces is introduced and studied by means of preclosed sets. itpreserves some fundamental properties of connected set in general topology.especially the famous k. fan’s theorem holds.

The aim of this paper is to introduce and study two new classes of spaces, called g∗-pre regular and g∗-pre normal spaces. Some basic properties of these separation axioms are studied by utilizing g∗-preclosed and g∗-preopen sets. A subset A of a space X is called g∗-preclosed (briefly g∗p-closed) set if pcl(A) ⊆ U whenever A ⊆ U and U is g-open in X. Mathematics Subject Classification: 54D10, ...

In this paper, a certain new connectedness of L-fuzzy subsets inL-topological spaces is introduced and studied by means of preclosed sets. Itpreserves some fundamental properties of connected set in general topology.Especially the famous K. Fan’s Theorem holds.

This paper is devoted to introduce and investigate some weak forms of fuzzy open mappings, namely fuzzy faintly semi open (fuzzy faintly semi closed), fuzzy faintly preopen (fuzzy faintly preclosed), fuzzy faintly α-open (fuzzy faintly α-closed), fuzzy faintly semi preopen (fuzzy faintly semi preclosed) and fuzzy faintly spopen (fuzzy faintly spclosed) mappings and their fundamental properties ...

In this paper, we introduce and characterize double fuzzy weakly preopen and double fuzzy weakly preclosed functions between I-double gradation fuzzy topological spaces and also study these functions in relation to some other types of already known functions.

We introduce r -fuzzy strongly preopen and r -fuzzy strongly preclosed sets in fuzzy topological space in view of the definition of Šostak (1985). We investigate some properties of them. Moreover, the concepts of fuzzy SP-continuous, fuzzy SP-irresolute continuous, fuzzy SP-irresolute open (closed) mappings, and a fuzzy SP-irresolute homeomorphism are introduced and studied. Some of their chara...

In this paper, the theory of Oθ-convergence and weak Oθ-convergence of nets is introduced in L-spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi’s O-convergence. It can be used to characterize preclosed sets, preopen sets, θ-closed sets, θ-open sets, almost F -compactness and almost S-compactness.