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sL-approximation spaces capture sL-domains

Published online by Cambridge University Press:  04 April 2025

Guojun Wu Open the ORCID record for Guojun Wu [Opens in a new window] ,
Luoshan Xu  and
Wei Yao
Guojun Wu*
Affiliation:
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
Luoshan Xu
Affiliation:
College of Mathematical Science, Yangzhou University, Yangzhou, China
Wei Yao
Affiliation:
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
*
Corresponding author: Guojun Wu; Email: guojunwu2023@163.com
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Abstract

In this paper, by means of upper approximation operators in rough set theory, we study representations for sL-domains and its special subclasses. We introduce the concepts of sL-approximation spaces, L-approximation spaces, and bc-approximation spaces, which are special types of CF-approximation spaces. We prove that the collection of CF-closed sets in an sL-approximation space (resp., an L-approximation space, a bc-approximation space) ordered by set-theoretic inclusion is an sL-domain (resp., an L-domain, a bc-domain); conversely, every sL-domain (resp., L-domain, bc-domain) is order-isomorphic to the collection of CF-closed sets of an sL-approximation space (resp., an L-approximation space, a bc-approximation space). Consequently, we establish an equivalence between the category of sL-domains (resp., L-domains) with Scott continuous mappings and that of sL-approximation spaces (resp., L-approximation spaces) with CF-approximable relations.

Keywords

Upper approximation operatorsL-domainsL-approximation spaceL-domaincategorical equivalence

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 35 , 2025 , e4
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

*

Supported by the National Natural Science Foundation of China (12231007, 12371462, 11671008), the Natural Science Foundation of Jiangsu Province (BK20170483).

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