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- W3165210112 abstract "We introduce a notion of strong proximity join-semilattice, a predicative notion of continuous lattice which arises as the Karoubi envelop of the category of algebraic lattices. Strong proximity join-semilattices can be characterised by the coalgebras of the lower powerlocale on the wider category of proximity posets (also known as abstract bases or R-structures). Moreover, locally compact locales can be characterised in terms of strong proximity join-semilattices by the coalgebras of the double powerlocale on the category of proximity posets. We also provide more logical characterisation of a strong proximity join-semilattice, called a strong continuous finitary cover, which uses an entailment relation to present the underlying join-semilattice. We show that this structure naturally corresponds to the notion of continuous lattice in the predicative point-free topology. Our result makes the predicative and finitary aspect of the notion of continuous lattice in point-free topology more explicit." @default.
- W3165210112 created "2021-06-07" @default.
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- W3165210112 date "2020-06-01" @default.
- W3165210112 modified "2023-09-26" @default.
- W3165210112 title "Predicative theories of continuous lattices" @default.
- W3165210112 hasPublicationYear "2020" @default.
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