相关论文: A generalization of Gelfand-Naimark-Stone 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…

We introduce the notion of a Nachbin proximity on a bounded archimedean $\ell$-algebra (bal-algebra), and show that Gelfand duality lifts to yield a dual equivalence between the category of uniformly complete bal-algebras equipped with a…

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…

We extend Yosida's 1941 version of Stone-Gelfand duality to metrically complete unital lattice-ordered groups that are no longer required to be real vector spaces. This calls for a generalised notion of compact Hausdorff space whose points…

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…

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…

It is a classic result in modal logic that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a Stone topology such that the binary relation is continuous.…

De Vries duality yields a dual equivalence between the category of compact Hausdorff spaces and a category of complete Boolean algebras with a proximity relation on them, known as de Vries algebras. We extend de Vries duality to completely…

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…

We extend the Gelfand-Naimark duality of commutative C*-algebras, "A COMMUTATIVE C*-ALGEBRA -- A LOCALLY COMPACT HAUSDORFF SPACE" to "A C*-ALGEBRA--A QUOTIENT OF A LOCALLY COMPACT HAUSDORFF SPACE". Thus, a C*-algebra is isomorphic to the…

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…

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…

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 duality (Commutative $C^*$-algebras $\equiv$ Locally compact Hausdorff spaces) is extended to $C^*$-algebras $\equiv$ Quotient maps on locally compact Hausdorff spaces. Using this duality, we give for an \emph{arbitrary}…

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…

We establish two duality theorems which refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first theorem we prove that the category of left-handed skew Boolean algebras whose…

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…

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…

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 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)…