Guojun Wu ; Luoshan Xu - Representations of Domains via CF-approximation Spaces

entics:10420 - Electronic Notes in Theoretical Informatics and Computer Science, March 21, 2023, Volume 2 - Proceedings of ISDT 9 - https://doi.org/10.46298/entics.10420
Representations of Domains via CF-approximation SpacesArticle

Authors: Guojun Wu ; Luoshan Xu

    Representations of domains mean in a general way representing a domain as a suitable family endowed with set-inclusion order of some mathematical structures. In this paper, representations of domains via CF-approximation spaces are considered. Concepts of CF-approximation spaces and CF-closed sets are introduced. It is proved that the family of CF-closed sets in a CF-approximation space endowed with set-inclusion order is a continuous domain and that every continuous domain is isomorphic to the family of CF-closed sets of some CF-approximation space endowed with set-inclusion order. The concept of CF-approximable relations is introduced using a categorical approach, which later facilitates the proof that the category of CF-approximation spaces and CF-approximable relations is equivalent to that of continuous domains and Scott continuous maps.


    Volume: Volume 2 - Proceedings of ISDT 9
    Published on: March 21, 2023
    Accepted on: December 6, 2022
    Submitted on: December 2, 2022
    Keywords: Mathematics - Rings and Algebras,Computer Science - Artificial Intelligence,Computer Science - Information Theory,06B35, 18B35

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