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In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they form a natural generalization of Stone's representation theorem for Boolean algebras. These concepts are named in honor of Marshall Stone. Stone-type dualities also provide the foundation for pointless topology and are exploited in theoretical computer science for the study of formal semantics.
This article gives pointers to special cases of Stone duality and explains a very general instance thereof in detail.
of Stoneduality and explains a very general instance thereof in detail. Probably the most general duality that is classically referred to as "Stone duality"...
necessarily hold for every derivative algebra V. Stoneduality provides a category theoretic duality between Boolean algebras and a class of topological...
clopen sets of the Stone space are then precisely the complexes of the Stone representation. The area of mathematics known as Stoneduality is founded on the...
the opposite (or dual) of another category then one speaks of a duality of categories, and says that the two categories are dually equivalent. An equivalence...
problems like representation and duality. Well known results like the representation theorem for Boolean algebras and Stoneduality fall under the umbrella of...
pairwise Stone spaces. This duality, which is originally also due to Marshall H. Stone, generalizes the well-known Stoneduality between Stone spaces and...
a category-theoretic duality between the category of Boolean algebras (with homomorphisms as morphisms) and the category of Stone spaces (with continuous...
various representation theorems, often collected under the label of Stoneduality. As explained before, orders are ubiquitous in mathematics. However...
the study of distributive lattices. In particular, there is a duality ("Priestley duality") between the category of Priestley spaces and the category of...
generalization of Stone's famous representation theorem for Boolean algebras and as a specialization of the general setting of Stoneduality. A further important...
(descriptive set theory) Suslin's problem Absorption law Prewellordering StonedualityStone's representation theorem for Boolean algebras Specialization (pre)order...
Bauer, Andrej & Taylor, Paul (2009). "The Dedekind Reals in Abstract StoneDuality". Mathematical Structures in Computer Science. 19 (4): 757–838. CiteSeerX 10...
ideals, where R is a commutative ring, is not sober in general. Stoneduality, on the duality between topological spaces that are sober and frames (i.e. complete...
differ from that for sheaves (of sets). Soberification. The article on Stoneduality describes an adjunction between the category of topological spaces and...
algebras is dually equivalent to the category of Heyting spaces. This duality can be seen as restriction of the classical Stoneduality of bounded distributive...
complete Heyting algebra. Locales are also called frames and appear in Stoneduality and pointless topology. Locally finite poset. A partially ordered set...
article, and in category theory in general, ∞ = ω. EGA FGA SGA Abstract StoneDuality nLab, just as a higher-dimensional Wikipedia, started in late 2008;...
the American mathematician Marshall Stone in 1936 when he observed while writing up his celebrated Stoneduality theorem that the supposedly loose analogy...
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