Related papers: Stone Duality Type Theorems for MV-algebras with I…

Compact Hausdorff topological MV-algebras and Stone MV-algebras are completely characterized. We obtain that compact Hausdorff topological MV-algebras are product (both topological and algebraic) of copies $[0,1]$ with standard topology and…

We prove three new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with…

The concept of a state MV-algebra was firstly introduced by Flaminio and Montagna in \cite{FlMo0} and \cite{FlMo} as an MV-algebra with internal state as a unary operation. Di Nola and Dvure\v{c}enskij gave a stronger version of a state…

We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between…

In this paper we prove some new Stone-type duality theorems for some subcategories of the category $\ZLC$ of locally compact zero-dimensional Hausdorff spaces and continuous maps. These theorems are new even in the compact case. They…

In this note we shall generalize the Stone duality between compact totally disconnected spaces and Boolean algebras to a duality between all complete non-Archimedean uniform spaces and Boolean algebras.

Stone duality establishes a contravariant equivalence between the category of Boolean algebras and the category of compact, Hausdorff, totally disconnected topological spaces (Stone spaces). These spaces are precisely the profinite spaces…

The notions of a {\em 2-precontact space}\/ and a {\em 2-contact space}\/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It is shown that there are bijective correspondences between…

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…

We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators…

Extensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental in proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions,…

Under a general categorical procedure for the extension of dual equivalences as presented in this paper's predecessor, a new algebraically defined category is established that is dually equivalent to the category $\bf LKHaus$ of locally…

It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that KH^op is equivalent to a…

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…

As a topological generalization of the notion of a multiset, a boolean multispace is a boolean space $X$ with a continuous function $u\colon X\to \mathbb Z_{>0}$, where $\mathbb Z_{>0}=\{1,2,\dots\}$ has the discrete topology. In this paper…

We present a Stone duality for bitopological spaces in analogy to the duality between Stone spaces and Boolean algebras, in the same vein as the duality between d-sober bitopological spaces and spatial d-frames established by Jung and…

It is proved that the category $\mathbb{EM}$ of extended multisets is dually equivalent to the category $\mathbb{CHMV}$ of compact Hausdorff MV-algebras with continuous homomorphisms, which is in turn equivalent to the category of complete…

The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour…

We introduce a two-sorted algebraic theory whose models are states of MV-algebras and, to within a categorical equivalence that extends Mundici's well-known one, states of Abelian lattice-groups with (strong order) unit. We discuss free…

We introduce a contravariant idempotent adjunction between (i) the category of ranked monads on $\mathsf{Set}$; and (ii) the category of internal categories and internal retrofunctors in the category of locales. The left adjoint takes a…