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.

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 theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces, and regular valuations on coherent so...