3 citations · 7 across the 17 of their papers we have counts for
23 papers
Generalizing Gelfand duality to Nachbin spaces
G. Bezhanishvili, P. J. Morandi
We introduce the notion of a Nachbin proximity on a bounded archimedean -algebra (bal-algebra). We prove that Gelfand duality lifts to yield a dual equivalence between the ca…
Duality Theory for Bounded Lattices: A Comparative Study
Guram Bezhanishvili, Luca Carai, Patrick Morandi
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier…
A New Proof of the Joyal-Tierney Theorem
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
Heyting frames and Esakia duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We introduce the category of Heyting frames and show that it is equivalent to the category of Heyting algebras and dually equivalent to the category of Esakia spaces. This provides…
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other thi…
Remarks on Hyperspaces for Priestley Spaces
G. Bezhanishvili, J. Harding, P. J. Morandi
The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of releva…