What question did this study set out to answer?

The goal is to establish a categorical equivalence between QFS-domains and strong proximity lattices.

June 14, 2026Mathematical logic quarterly0 citations

The Representations of QFS‐Domains

FFFan FengHunan University ZYZhenzhu YuanChangsha Normal University QLQingguo LiHunan University

Key Points

The goal is to establish a categorical equivalence between QFS-domains and strong proximity lattices.
Develop the concept of strong proximity lattices.
Prove categorical equivalence between categories related to QFS-domains and strong proximity lattices.
Build on existing theories by Achim Jung and Philipp Sünderhauf.
Successfully demonstrate that QFS-domains and strong proximity lattices are categorically equivalent.
Answer a question previously posed by Achim Jung at ISDT'13.

Abstract

ABSTRACT In this paper, we propose the strong* proximity lattices, and prove that the categories and are categorically equivalent, building on the framework established by Achim Jung and Philipp Sünderhauf. denotes the category of all QFS‐domains and continuous functions. denotes the category of the strong* proximity lattices with the approximable relations. This answers the question posed by Achim Jung at the conference ISDT'13.

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