We study structures called d-frames which were developed by the last two authors for a bitopological treatment of Stone duality. These structures consist of a pair of frames thought of as the opens of two topologies, together with two relations which serve as abstractions of disjointness and covering of the space. With these relations, the topological separation axioms regularity and normality ...

The aim of this paper is to introduce the concept of Λ operator of a fuzzy set in a fuzzy bitopological space.Then we study (i, j)-fuzzy Λγ -set and its properties. Moreover, we define (i, j)-fuzzy Λ-closed set, (i, j)-fuzzy Λγ -closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts of (i, j)-fuzzy Λ-closed set and (i, j)-fuzzy generalized closed set are i...

It is well known [Hoc69, Joy71] that profinite T0-spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space. (2) The T0-reflection of (X,τ) is a profinite T0-space. (3) (X,τ) is a quasi spectral space (in the sense of [BMM08]). (4) (X,τ) admits a ...

We modify the concept of θ-regularity for spaces with 2 and 3 topologies. The new, more general property is fully preserved by sums and products. Using some bitopological reductions of this property, Michael’s theorem for several variants of bitopological paracompactness is proved.

In this paper, we built bitopological space on the concept of neutrosophic soft set, defined basic topological concepts spaces which are N3-(bi)*-open N3-(bi)*-closed (bi)*-neutrosophic interior, (bi)* closure, boundary, exterior and introduced their properties. addition, investigated relations these with counterparts in many examples.

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pseudo Uryshon) - fs bicsp's introduced both their induced bitopological spaces. It shown that hereditary property satisfied for with respect to but other mentioned types separations satisfies clos...

In this paper we continue to research relationships between closure-type properties of hyperspaces over a space X and covering X. For Hausdorff denote by 2X the family all closed subsets We investigate selection bitopological (2X, Δ1+ , Δ2+) where Δi+ is upper Δi-topology for each i=1,2.

The notion of δ−open sets in bitopological spaces was introduced by Banerjee [2]. In this paper we more investigate ij− δ−open sets. We study some sets related to ij− δ−open sets. Also, we study some separation axioms in bitopological spaces based on ij − δ−open sets.