International Journal of Nonlinear Analysis and Applications

Pairwise compactness in bi-isotonic spaces

Document Type : Research Paper

Authors

Sakarya University, Faculty of Science, Department of Mathematics, 54050 Sakarya, Turkey

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

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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