Comment on L-convergence spaces via L-ordered co-Scott closed sets

Lingqiang, Li; Qiu, Jin

doi:10.22111/ijfs.2025.49905.8815

Document Type : Research Paper

Authors

Li Lingqiang ¹
Jin Qiu ²

¹ Department of Mathematics, Liaocheng University

² Liaocheng University

https://doi.org/10.22111/ijfs.2025.49905.8815

Abstract

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.

Keywords

Main Subjects

Fuzzy Math

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Comment on L-convergence spaces via L-ordered co-Scott closed sets

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Volume 22, Issue 1January and February 2025Pages 131-134

Volume 22, Issue 1
January and February 2025
Pages 131-134