Volume 26 , Issue 2 , PP: 299-309, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Ali A. Atoom 1 * , Hamza Qoqazeh 2 , Eman Hussein 3 , Anas Owledat 4
Doi: https://doi.org/10.54216/IJNS.260223
It is essential to create new mathematical strategies to deal with everyday problems since they require a lot of data and ambiguity. The best tool for doing this is proper functions, which are the most common mathematical technique. In order to generate suitable functions, we investigate several set operators. A connection between symmetry and certain types of proper functions and their classical topologies can be made. As a result of this symmetry, we can examine the traits and behaviors of traditional topological notions through settings, and vice versa. We describe a new class of proper functions in this paper and launch a preliminary investigation into them. These functions are referred to as pairwise local proper functions and pairwise local Lindel¨of proper functions in bitopological spaces. In general topology, we also establish the connection between this new class of proper functions and other classes of generalized functions already in existence. Regarding the new ideas, a number of relationships, necessary and sufficient conditions, examples and counter-examples are provided. In addition, a different argument for the pairwise regularity of a pairwise Hausdorff and pairwise locally compact bitopological space is presented. As part of this research, we also look at the images and inverse images of specific bitopological features under these functions. A few product theorems pertaining to these concepts were finally discovered.
Bitopological spaces , Pairwise locally compact , Pairwise local lindelö , f , Pairwise proper function , Pairwise locally proper functions , Pairwise local Lindelö , proper functions
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