Predicative theories of continuous lattices

Predicative theories of continuous lattices

Blog Article

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 here 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 vegetable glycerin for sale 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.