Applications of Scott-closed sets in convex structures

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Article
Citation
Yue, Y., Yao, W., & Ho, W. K. (2022). Applications of Scott-closed sets in convex structures. Topology and its Applications, 314, Article 108093. https://doi.org/10.1016/j.topol.2022.108093
Author
Yue, Yueli
•
Yao, Wei
•
Ho, Weng Kin 
Abstract
The aim of this paper is to show that Scott-closed sets have a good application in convex structures. Firstly, based on remotehood system, we give a characterization of convex structure by the Kleisli monoid with respect to the Scott-closed set monad. Then, by an op-canonical lax extension of the Scott-closed set monad, we introduce convex convergence spaces and prove that convex structures are precisely the reflexive and transitive lax algebras. Finally, we study the relationship between ordered structures and separated convex structures.
Keywords
Date Issued
2022
Publisher
Elsevier
Journal
Topology and its Applications
DOI
10.1016/j.topol.2022.108093