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.

In [7] some results concerning S-splitting, S-jointly continuous, D-splitting and D-jointly continuous topologies are considered, where S and D are the Sierpinski space and the double-point space, respectively. Here we generalize these results replacing the spaces S and D by any finite space. 2000 AMS Classification: 54C35.

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.

In this article we introduce the notion of fuzzy b-locally open (bLO) sets, fuzzy bLO sets, fuzzy bLO sets in fuzzy bitopological spaces and obtain several characterizations and some properties of these sets. Also we introduce the notion of fuzzy b-locally continuous functions on bitopological spaces.

An Ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. In this paper, (i,j)g*s closed and open sets are introduced with respect to an ideal in a bitopological space and their properties are investigated. Additionally, we compare them with other sets to show their relationships and characterize many other results.

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...