Distance Domains: Continuity

TL;DR

This paper extends classical domain theory to quantitative domains using the abstract basis approach, providing new dual characterisations of distance domains and unifying previous formal ball dualities.

Contribution

It introduces dual characterisations of distance domains and unifies existing formal ball dualities within the framework of quantitative domain theory.

Findings

New dual characterisations of distance domains

Unified formal ball dualities for quantitative domains

Characterisation of hemimetric spaces with Smyth completion

Abstract

We take the abstract basis approach to classical domain theory and extend it to quantitative domains. In doing so, we provide dual characterisations of distance domains (some new even in the classical case) as well as unifying and extending previous formal ball dualities, namely the Kostanek-Waszkiewicz and Romaguero-Valero theorems. In passing, we also characterise hemimetric spaces that admit a hemimetric Smyth completion.