Considering a countable number of topologies on a set X, we introduce the notion of (א0)topological spaces as a generalization of the notions of both bitopological spaces and (ω)topological spaces, and study some of their properties. AMS Mathematics Subject Classification (2000): 54A10

In this paper we define pairwise-$\alpha$-paracompact subsets as a generalisation of $\alpha$-paracompact in topological spaces and study their properties its relations with other bitopological spaces. Several theorems are obtained concerning sets. We introduced the definition $p$-paracompact bitoplogical

The concept of pairwise S-closedness in bitopological spaces has been introduced and some properties of such spaces have been studied in this paper. EY WORDS AND PHRASES. Pairwise semi-open, Pairwise almost compact, Pairwise S-closed, Pairwise regularly open and regularly closed, Pairwise extremal disconnectedness, Pairwise semi-continuous and irresolute functions. 1980 AMS MATHEMATICS SUBJECT ...

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.

We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regularLindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish so...