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

Document Type : Research Paper

Authors

1 Department of Mathematics, Liaocheng University

2 Liaocheng University

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

References

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Iranian Journal of Fuzzy Systems
Volume 22, Issue 1
January and February 2025
Pages 131-134

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