Locally pairwise paracompact spaces and locally nearly pairwise paracompact spaces.

We introduce the concept of a pairwise locally paracompact and pairwise locally nearly paracompact spaces in bi-topological spaces if 푋=(푋, τ1, τ2) be a bi-topological space, and let i ≠ j, i,j = 1,2, then X is called τi-locally paracompact with respect to τ푗 if every point of X has a τ푖−open neighborhood whose τ푗−closure is pairwise paracompact. A bi-topological space 푋=(푋, τ1, τ2) is said to be pairwise locally paracompact if it is τi-locally paracompact with respect to τj, for every i≠j, i, j= 1,2. A space X is pairwise locally nearly paracompact if and only if each point x of 푋 has an P- open neighbourhood 푈 such that cl(U) (In τ1 표푟 τ2) is α-nearly pairwise paracompact. Then i study their properties and their relations with other topological spaces. Several examples are discussed. [ABSTRACT FROM AUTHOR]