相关论文: Hofmann-Lawson duality for locally small spaces
In [G. Dimov and E. Ivanova-Dimova, Two extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces, arXiv:1901.04537v4, 1--33], extending the Stone Duality Theorem, we proved two duality theorems for the category…
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.
Inspired by classic work of Wallman and more recent work of Jung-Kegelmann-Moshier and Vickers, we show how to encode general subbases of stably locally compact spaces via certain entailment relations. We further build this up to a…
The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski topos. In this paper we apply such techniques to the higher…
The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the…
The aim of the present paper is to extend the dualizing object approach to Stone duality to the non-commutative setting of skew Boolean algebras. This continues the study of non-commutative generalizations of different forms of Stone…
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…
We consider local Gorenstein duality for cochain spectra $C^*(BG;R)$ on the classifying spaces of compact Lie groups $G$ over complex orientable ring spectra $R$. We show that it holds systematically for a large array of examples of ring…
We extend Stone duality to a fully faithful embedding of condensed sets into fpqc sheaves over an arbitrary field, which preserves colimits and finite limits. We study how familiar notions from condensed mathematics/topology and algebraic…
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 show explicitly that Boolean inverse semigroups are in duality with what we term Boolean groupoids. This generalizes the classical Stone duality, which we refer to as commutative Stone duality, between generalized Boolean algebras and…
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…
In this paper we provide spectral inclusion and mapping theorems for strongly continuous locally equicontinuous semigroups on Hausdorff locally convex spaces. Our results extend the classical spectral inclusion and mapping theorems for…
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the…
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…
We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein…
We establish a duality between global sheaves on spectral spaces and right distributive bands. This is a sheaf-theoretical extension of classical Stone duality between spectral spaces and bounded distributive lattices. The topology of a…
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 locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…
In three recaent papers of G. Dimov, many Stone-type duality theorems for the category of locally compact Hausdorff spaces and continuous maps and some of its subcategories were proved. The dual objects in all these theorems are the local…