in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.

We introduce strong separation axioms in bitopological spaces. We also introduce the notion of strong pairwise compactness.

By using the notion of m-spaces, we establish the unified theory for several variations of separation axioms quasi T0, quasi T1 and quasi T2 in bitopological spaces.

Bimodal provability logic GLB, introduced by G. Japaridze, currently plays an important role in the applications of provability logic to proof-theoretic analysis. Its topological semantics interprets diamond modalities as derived set operators on a bi-scattered bitopological space. We study the question of completeness of this logic w.r.t. the most natural space of this kind, that is, w.r.t. an...

The purpose of this paper is to introduce the notions g̃-R0, g̃-R1, g̃-T0, g̃-T1 and g̃-T2 in bitopological spaces.

We present a Stone duality for bitopological spaces in analogy to the duality between topological spaces and frames, and discuss the resulting notions of sobriety and spatiality. Under the additional assumption of regularity, we prove a characterisation theorem for subsets of a bisober space that are compact in one and closed in the other topology. This is in analogy to the celebrated Hofmann-M...

We obtain the further properties of quasi Mcontinuous functions which were introduced and investigated in order to establish the unified theory for several variations of quasi-continuity between bitopological spaces.

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.