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Comment on L-convergence spaces via L-ordered co-Scott closed sets | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 22، شماره 1، فروردین و اردیبهشت 2025، صفحه 131-134 اصل مقاله (332.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2025.49905.8815 | ||
| نویسندگان | ||
| Li Lingqiang1؛ Jin Qiu* 2 | ||
| 1Department of Mathematics, Liaocheng University | ||
| 2Liaocheng University | ||
| چکیده | ||
| Han and Pang (IJFS 2024) introduced important L-convergence structures based on L- ordered co-Scott closed sets, extending strong L-concave structures. Since L-ordered co- Scott closed sets and L-convergence structures rely on L-order, while strong L-concave structures depend on pointwise order, the relationship between them is still not clear enough. To clarify this, we provide characterizations of both using pointwise orders, re- vealing that the definition of L-ordered co-Scott closed sets can be simplified, as its strat- ified condition can be derived from the L-ordered condition. This finding will streamline proofs in Han and Pang’s paper, as these conditions have been repeatedly verified. Addi- tionally, our insights will aid in accurately establishing the relationships between various lattice-valued co-Scott closed sets and lattice-valued concave structures. | ||
| کلیدواژه‌ها | ||
| L-convex space؛ L-concave space؛ L-ordered co-Scott closed set؛ L-convergence space | ||
| مراجع | ||
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[9] X. Y. Wu, Y. W. Huang, L-convex convergence relation and L-convex ideal-convergence structure, Iranian Journal of Fuzzy Systems, 21(5) (2024), 31-49. https://doi.org/10.22111/ijfs.2024.49227.8679 [10] X. Y. Wu, E. Q. Li, Characterizations of L-concavities and L-convexities via derived relations, Hacettepe Journal of Mathematics and Statistics, 52(4) (2023), 876-895. https://doi.org/10.15672/hujms.1175332 [11] Z. Y. Xiu, Convergence structures in L-concave spaces, Journal of Nonlinear and Convex Analysis, 21(12) (2020), 2693-2703. [12] L. Zhang, B. Pang, Strong L-concave structures and L-convergence structures, Journal of Nonlinear and Convex Analysis, 21(12) (2021), 2759-2769. [13] L. Zhang, B. Pang, Convergence structures in (L,M)-fuzzy convex spaces, Filomat, 37 (2023), 2859-2877. https: //doi.org/10.2298/FIL2309859Z | ||
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