Representations of Domains via CF-approximation Spaces
Abstract
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.
Keywords
Cite
@article{arxiv.2211.17099,
title = {Representations of Domains via CF-approximation Spaces},
author = {Guojun Wu and Luoshan Xu},
journal= {arXiv preprint arXiv:2211.17099},
year = {2023}
}
Comments
13pages, an interaction of Mathematics and information science