Related papers: Stone-Gelfand duality for metrically complete latt…
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…
Generalizing Duality Theorem of V. V. Fedorchuk, we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous…
Gelfand-Naimark-Stone duality establishes a dual equivalence between the category ${\sf KHaus}$ of compact Hausdorff spaces and the category ${\boldsymbol{\mathit{uba}\ell}}$ of uniformly complete bounded archimedean $\ell$-algebras. We…
We characterize those algebras over a disconnected uniformly complete topological field which are representable as algebras of continuous functions on compact topological spaces, generalizing thus Gelfand duality for non-archimedean normed…
We extend the classical Stone duality between zero dimensional compact Hausdorff spaces and Boolean algebras. Specifically, we simultaneously remove the zero dimensionality restriction and extend to \'etale groupoids, obtaining a duality…
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…
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…
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…
The classical Stone duality associates to each Boolean algebra a topological space consisting of ultrafilters. Lawson's generalisation constructs a dual equivalence of categories of Boolean inverse $\land$-semigroups and Hausdorff ample…
In this note we prove Yosida duality --- that is: the category of compact Hausdorff spaces with continuous maps is dually equivalent to the category of uniformly complete Archimedean Riesz spaces with distinguished units and unit-preserving…
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…
Stone's representation theorem asserts a duality between Boolean algebras on the one hand and Stone space, which are compact, Hausdorff, and totally disconnected, on the other. This duality implies a natural isomorphism between the…
Stone duality is an indispensable tool for the study of compact, zero-dimensional, Hausdorff spaces. In the case of general compact Hausdorff spaces one can get quite a bit of mileage by considering the `Wallman duality' between compact…
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…
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…
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…
Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…
Open sets and compact saturated sets enjoy a perfect formal symmetry, at least for classes of spaces such as Stone spaces or spectral spaces. For larger classes of spaces, a perfect symmetry may not be available, although strong signs of it…
In this paper we introduce the concept of MV-topology, a special class of fuzzy topological spaces, and prove a proper extension of Stone Duality to the categories of limit cut complete MV-algebras and Stone MV-spaces, namely,…
Stone duality generalizes to an equivalence between the categories $\mathsf{Stone}^{\mathsf{R}}$ of Stone spaces and closed relations and $\mathsf{BA}^\mathsf{S}$ of boolean algebras and subordination relations. Splitting equivalences in…