arXiv subjects

P. J. Morandi

Publications and source records attributed to P. J. Morandi.

3 recordsLinked to original sources

arXiv2026

Generalizing Gelfand duality to Nachbin spaces

We introduce the notion of a Nachbin proximity on a bounded archimedean $\ell$-algebra (bal-algebra). We prove that Gelfand duality lifts to yield a dual equivalence between the categories of uniformly complete bal-algebras equipped with a closed Nachbin proximity and of Nachbin spaces (compact ordered spaces). The key ingredients of the proof include appropriate generalizations of the Stone-Weierstrass theorem and Dieudonn\'{e}'s lemma. We also develop an alternate approach by means of bounded archimedean $\ell$-semialgebras (sbal-algebras), from which we derive De Rudder--Hansoul duality.

math.AC↗

arXiv2022

Remarks on Hyperspaces for Priestley Spaces

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 relevant hyperspace constructions based on various topologies on a Priestley space and mechanisms to topologize the hyperspace of closed sets. A number of authors considered hyperspaces of Priestley spaces and their application to the coalgebraic approach to positive modal logic. A mixture of techniques from category theory, pointfree topology, and Priestley duality have been employed. Our aim is to provide a unifying approach to this area of research relying only on a basic familiarity with Priestley duality and related free constructions of distributive lattices.

math.GN↗

arXiv2019

Gelfand-Naimark-Stone duality for normal spaces and insertion theorems

Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean $\ell$-algebras. In [4] we extended this duality to completely regular spaces. In this article we use this extension to characterize normal, Lindëlof, and locally compact Hausdorff spaces. Our approach gives a different perspective on the classical theorems of Katětov-Tong and Stone-Weierstrass.

math.GN↗