Based on the theory of frames we introduce a Stone duality for bitopological spaces. The central concept is that of a d-frame, which axiomatises the two open set lattices. Exploring the resulting concept of d-sobriety we find this to be a much more inclusive concept than usual sobriety. Spatial d-frames suggest additional axioms that lead us to define reasonable d-frames; these have an alternat...

Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...

Building on earlier work by Guo-Qiang Zhang on disjunctive information systems, and by Thomas Ehrhard, Pasquale Malacaria, and the first author on stable Stone duality, we develop a framework of disjunctive propositional logic in which theories correspond to algebraic L-domains. Disjunctions in the logic can be indexed by arbitrary sets (as in geometric logic) but must be provably disjoint. Thi...

Extending the Stone Duality Theorem, we prove two duality theorems for category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They extend also Tarski Theorem; latter is even derived from one them. We as well new EDTych extremally disconnected Tychonoff Also, describe categories which are dually equivalent to ZComp compactifications obtain a corollary Dwinger Theorem about space.

We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A positive consequence of the choice of morphisms is that those on the topological side are functional. Towards obtaining the topological duality, we develop a unive...

This paper establishes a Stone-type duality between specifications and infLMPs. An infLMP is a probabilistic process whose transitions satisfy super-additivity instead of additivity. Interestingly, its simple structure can encode a mix of probabilistic and non-deterministic behaviors. Our duality shows that an infLMP can be considered as a demonic representative of a system’s information. Moreo...

Stone duality generalizes to an equivalence between the categories StoneR of spaces and closed relations BAS boolean algebras subordination relations. Splitting equivalences in yields a category that is equivalent KHausR compact Hausdorff Similarly, splitting DeVS de Vries compatible Applying machinery allegories then DeVS, thus resolving problem recently raised literature. The further restrict...