Paper Title
ANALYZING THE LOCALLY PARACOMPACTNESS AND LOCALLY NEARLY PARACOMPACTNESS IN BITOPOLOGICAL SPACES

Abstract
This research advances the concept, characteristics, and theoremsof compactness in bitopologicalspacesby introducing a special typeof covering that incorporates novel and impact properties of locally paracompact and locally nearly paracompactin bitopologicalspaces. Specifically, ifξ = (ξ,℘_1,℘_2)is a bitopological space, and if i≠ j,i,j= 1,2, then 𝜉 is called ℘i- locally paracompact with respect to ℘_j if every point of 𝜉 has a ℘_(i-)open neighborhood whose ℘_(j-)closure is pairwise paracompact. A bitopological space ξ = (ξ,℘_1,℘_2)is said to be pairwise locally paracompact if it is ℘i-locally paracompact with respect to ℘j, for every i≠j, i,j= 1,2. A space 𝜉 is pairwise locally nearly paracompact if and only if each point x of 𝜉 has an P-open neighborhood U such that cl(U) (in ℘_1or℘_2) is α-nearly pairwise paracompact. Moreover, this study was also exploring the properties of locally paracompact and locally nearly paracompactin bitopologicalspaces, and examines their relations with other known topological spaces. Several examples are discussed.As a result, several new properties such as pairwise locally paracompact space, and pairwise locally nearly paracompact spaces were established. Keywords - Pairwise paracompact space, pairwise locally paracompact space, pairwise locally nearly paracompact.