# Representations of Domains via CF-approximation Spaces

arXiv: https://arxiv.org/abs/2211.17099 · HTML: https://mlsanity.com/paper/2211.17099/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Builds on (most cited first, 1 of 1)

- [Continuous Domains in Formal Concept Analysis](https://mlsanity.com/paper/1912.04496/) (2019)

## Abstract (arXiv)

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.