Pairwise compactness in bi-isotonic spaces

Document Type : Research Paper

Authors
Soley Ersoy
Seval Koca
Sakarya University, Faculty of Science, Department of Mathematics, 54050 Sakarya, Turkey
10.22075/ijnaa.2024.32706.4867
Abstract
In this article, we have introduced the notion of pairwise compactness in bi-isotonic spaces via finite intersection property and pairwise open cover. Moreover, we have given pairwise compactness of bi-isotonic subspaces with both reduced closure and interior functions. We have characterized pairwise compactness by the neighborhood concept; however, the axioms of bi-isotonic spaces are insufficient to prove the theorem, and we have studied this in bi-closure spaces. For similar reasons, occasionally, bi-closure spaces have been considered with additional explanations, even if some concepts related to compactness have been naturally extended to bi-isotonic spaces. Additionally, interesting results have been obtained considering the pairwise Hausdorffness and compactness relationship. It has also been observed that resembling cross-relationships exist for closed subsets of pairwise compact spaces. Finally, it has been observed that the pairwise compactness of bi-closure spaces is preserved under bi-continuity.
Keywords
Pairwise compact
pairwise Hausdorff space
closure operator
bi-isotonic space
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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 6
June 2025
Pages 23-33

  • Receive Date 19 December 2023
  • Revise Date 17 January 2024
  • Accept Date 05 April 2024