Related papers: Gr\"atzer-Hofmann-Lawson-Jung-S\"underhauf Duality

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…

Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a…

A convexity space is a set X with a chosen family of subsets (called convex subsets) that is closed under arbitrary intersections and directed unions. There is a lot of interest in spaces that have both a convexity space and a topological…

We show that the following five categories are equivalent: (1) the opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales; (5)…

Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. Both of them imply easily the Tarski Duality Theorem, as well as two new duality theorems…

A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.

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…

A closed real subspace V of a complex Hilbert space H is called standard if V intersects iV trivially and and V + i V is dense in H. In this note we study several aspects of the geometry of the space Stand(H) of standard subspaces. In…

Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called…

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…

We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…

We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Keimel and Lawson. This allows us to describe their Stone duals explicitly. As another application, we show that…

Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category $\bf KHaus$ of compact Hausdorff spaces and their continuous maps, as an extension of a…

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…

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…

We consider smooth, complex quasi-projective varieties $U$ which admit a compactification with a boundary which is an arrangement of smooth algebraic hypersurfaces. If the hypersurfaces intersect locally like hyperplanes, and the relative…

In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs from the set-theoretic one. Here we…

A common feature of many duality results is that the involved equivalence functors are liftings of hom-functors into the two-element space resp. lattice. Due to this fact, we can only expect dualities for categories cogenerated by the…

Recently in \cite{FM, FlMo}, the language of MV-algebras was extended by adding a unary operation, an internal operator, called also a state-operator. In \cite{DD1}, a stronger version of state MV-algebras, called state-morphism MV-algebras…

By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras. In our recent article, we have extended de Vries duality to completely regular spaces by generalizing de Vries algebras…