@article{Yao2025, 
author = {Lingjuan Yao},
title = {Stably continuous semilattices in closure spaces},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {17483-17493},
keywords = {categorical equivalence, stably continuous semilattices, generalized directed sets, S-closure spaces},
url = {https://www.sciopen.com/article/10.3934/math.2025781},
doi = {10.3934/math.2025781},
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.}
}