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...

A topological space X, τ is said to be strongly compact if every preopen cover of X, τ admits a finite subcover. In this paper, we introduce a new class of sets called N-preopen sets which is weaker than both open sets and N-open sets. Where a subset A is said to be N-preopen if for each x ∈ A there exists a preopen set Ux containing x such that Ux − A is a finite set. We investigate some prope...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

The concept of a preopen set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called preopen or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called preclosed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, preopen, was used for the first time by A. S. Mashhour, M. E. Abd El-Monse...

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF mprecontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

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 ...

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, ...

The goal of this paper is to investigate the certain properties bipolar fuzzy supra preopen sets (BF set). We introduce and study concepts pre-interior pre-interior) pre-closure pre-closure) operators. Furthermore, we define new type continuous mapping based on BF sets.

In this paper we have introduced the concept of (γ, γ′)-preopen sets in topological space.