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