Enriched closure spaces as a novel framework for domain theory

2017/05/14 by Paul Poncet, Poncet, Paul
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Logic in Computer Science (cs.LO) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1705.04945

openalex publication_date 2017/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a generalization of continuous lattices and domains through the concept of enriched closure space, defined as a closure space equipped with a preclosure operator satisfying some compatibility conditions. In this framework we are able to define a notion of way-below relation; an appropriate definition of continuity then naturally follows. Characterizations of continuity of the enriched closure space and necessary and sufficient conditions for the interpolation property are proved. We also draw a link between continuity and the possibility for the subsets that are open with respect to the preclosure operator to form a topology.

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