Stably continuous semilattices in closure spaces

Lingjuan Yao; Lingjuan Yao

doi:10.3934/math.2025781

AIMS Mathematics

2025, Volume 10, Issue 8: 17483-17493. doi: 10.3934/math.2025781

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Research article

Stably continuous semilattices in closure spaces

Lingjuan Yao ^{1,2
,
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1.
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China
2.
Gansu Center for Fundamental Research in Complex Systems Analysis and Control, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China

Received: 09 April 2025 Revised: 16 July 2025 Accepted: 24 July 2025 Published: 01 August 2025
MSC : 06B35, 54A05

In this paper, we introduce the concept of S-closure spaces and demonstrate that they precisely generate stably continuous semilattices. Additionally, we define the notion of S-morphisms between S-closure spaces to represent Scott continuous functions between stably continuous semilattices. These developments establish an equivalence between the category of stably continuous semilattices and the category of S-closure spaces with S-morphisms as the morphisms. This result provides a method for representing stably continuous semilattices through the framework of closure spaces.
- categorical equivalence,
- stably continuous semilattices,
- generalized directed sets,
- S-closure spaces
Citation: Lingjuan Yao. Stably continuous semilattices in closure spaces[J]. AIMS Mathematics, 2025, 10(8): 17483-17493. doi: 10.3934/math.2025781

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Abstract

In this paper, we introduce the concept of S-closure spaces and demonstrate that they precisely generate stably continuous semilattices. Additionally, we define the notion of S-morphisms between S-closure spaces to represent Scott continuous functions between stably continuous semilattices. These developments establish an equivalence between the category of stably continuous semilattices and the category of S-closure spaces with S-morphisms as the morphisms. This result provides a method for representing stably continuous semilattices through the framework of closure spaces.

References

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