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Pairwise compactness in bi-isotonic spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 3، دوره 16، شماره 6، شهریور 2025، صفحه 23-33 اصل مقاله (388.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32706.4867 | ||
| نویسندگان | ||
| Soley Ersoy* ؛ Seval Koca | ||
| Sakarya University, Faculty of Science, Department of Mathematics, 54050 Sakarya, Turkey | ||
| تاریخ دریافت: 28 آذر 1402، تاریخ بازنگری: 27 دی 1402، تاریخ پذیرش: 17 فروردین 1403 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Pairwise compact؛ pairwise Hausdorff space؛ closure operator؛ bi-isotonic space | ||
| مراجع | ||
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[1] T. Bırsan, Compacite dans les espaces bitopologiques, An. Sti. Univ. Al. I. Cuza Iasi Sect. I Mat. (N.S.) 15 (1969), 317–328. [2] C. Boonpok, ∂−closed sets in biclosure spaces, Acta Math. Univ. Ostrav. 17 (2009), 51–66. [3] C. Boonpok, On closed maps in bi Cech closure spaces, Int. Math. Forum 4 (2010), 2161–2167. [4] S. Ersoy and A.A. Acet, Pairwise connectedness in bi-isotonic spaces, Palest. J. Math. 11 (2022), no. 2, 342––351. [5] S. Ersoy and N. Erol, Separation axioms in bi-isotonic spaces, Sci. Math. Jpn. 83 (2020), no. 3, 225–240. [6] P. Fletcher, H.B. Hoyle, and C.W. Patty, The comparison of topologies, Duke Math. J. 36 (1969), 325–331. [7] E.D. Habil and K.A. Elzenati, Connectedness in isotonic spaces, Turk. J. Math. 30 (2006), no. 3, 247—262. [8] J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. 13 (1963), no. 1, 71–89. [9] Y.W. Kim, Pairwise compactness, Publ. Math. Debrecen 15 (1968), no. 1-4, 87–90. [10] K. Kuratowski, Topology, vol. I, Academic Press; Warszawa: PWN—Polish Scientific Publishers, New York-London, 1966. [11] L. Motchane, Sur la notion d’espace bitopologique et sur les espaces de Baire, C. R. Acad. Sci. Paris 224 (1957), 3121-3124. [12] A. Mukharjee and M.K. Bose, Some results on nearly pairwise compact spaces, Bull. Malays. Math. Sci. Soc. 39 (2016), 933—940. [13] D.H. Pahk and B.D. Choi, Notes on pairwise compactness, Kyungpook Math. J. 11 (1971), 45–52. [14] J. Saegrove, Pairwise complete regularity and compactification in bitopological spaces, J. London Math. Soc. (2) 7 (1973), 286––290. [15] B.M.R. Stadler and P.F. Stadler, Basic properties of closure spaces, J. Chem. Inf. Comput. Sci. 42 (2002), 577-585. [16] B.M.R. Stadler and P.F. Stadler, Higher separation axioms in generalized closure spaces, Comment. Math. (Prace Mat.) 43 (2003), 257–273. [17] J. Swart, Total disconnectedness in bitopological spaces and product bitopological spaces, Indag. Math. 33 (1971), 135–145. | ||
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