Distance domains: Continuity

0542021 - MÚ 2022 RIV NL eng J - Journal Article
Bice, Tristan
Distance domains: Continuity.
Theoretical Computer Science. Roč. 869, 12 May (2021), s. 85-107. ISSN 0304-3975. E-ISSN 1879-2294
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : abstract basis * continuous poset * distance
OECD category: Pure mathematics
Impact factor: 1.002, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.tcs.2021.01.038

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 show that hemimetric spaces admit a hemimetric Smyth completion precisely when they are Noetherian in a natural quantitative sense.
Permanent Link: http://hdl.handle.net/11104/0319517