Lattice-free and point-free: Vickers duality for subbases of stably locally compact spaces

0573344 - MÚ 2024 RIV NL eng J - Journal Article
Bice, Tristan - Kubiś, Wieslaw
Lattice-free and point-free: Vickers duality for subbases of stably locally compact spaces.
Theoretical Computer Science. Roč. 960, June (2023), č. článku 113895. ISSN 0304-3975. E-ISSN 1879-2294
R&D Projects: GA ČR(CZ) GF22-07833K; GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : entailment relations * stably locally compact spaces * stone duality
OECD category: Pure mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.tcs.2023.113895

Inspired by classic work of Wallman and more recent work of Jung-Kegelmann-Moshier and Vickers, we show how to encode general subbases of stably locally compact spaces via certain entailment relations. We further build this up to a categorical duality encompassing the classic Priestley-Stone duality and its various extensions to stably locally compact spaces by Shirota, De Vries, Hofmann-Lawson (in the stable case), Jung-Sünderhauf, Hansoul-Poussart, Bezhanishvili-Jansana, van Gool and Bice-Starling.
Permanent Link: https://hdl.handle.net/11104/0343807