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- Esakia_duality abstract "In mathematics, Esakia duality is the dual equivalence between the category of Heyting algebras and the category of Esakia spaces. Esakia duality provides an order-topological representation of Heyting algebras via Esakia spaces.Let Esa denote the category of Esakia spaces and Esakia morphisms.Let H be a Heyting algebra, X denote the set of prime filters of H, and ≤ denote set-theoretic inclusion on the prime filters of H. Also, for each a∈ H, let φ(a) = {x∈ X : a∈ x} , and let τ denote the topology on X generated by {φ(a), X − φ(a) : a∈ H}.Theorem: (X,τ,≤) is an Esakia space, called the Esakia dual of H. Moreover, φ is a Heyting algebra isomorphism from H onto the Heyting algebra of all clopen up-sets of (X,τ,≤). Furthermore, each Esakia space is isomorphic in Esa to the Esakia dual of some Heyting algebra.This representation of Heyting algebras by means of Esakia spaces is functorial and yields a dual equivalence between the category HA of Heyting algebras and Heyting algebra homomorphisms and the category Esa of Esakia spaces and Esakia morphisms.Theorem: HA is dually equivalent to Esa.".
- Esakia_duality wikiPageID "26600432".
- Esakia_duality wikiPageLength "2349".
- Esakia_duality wikiPageOutDegree "15".
- Esakia_duality wikiPageRevisionID "568479643".
- Esakia_duality wikiPageWikiLink Category:Lattice_theory.
- Esakia_duality wikiPageWikiLink Category:Topology.
- Esakia_duality wikiPageWikiLink Category_(mathematics).
- Esakia_duality wikiPageWikiLink Clopen_set.
- Esakia_duality wikiPageWikiLink Duality_theory_for_distributive_lattices.
- Esakia_duality wikiPageWikiLink Equivalence_of_categories.
- Esakia_duality wikiPageWikiLink Esakia_space.
- Esakia_duality wikiPageWikiLink Functor.
- Esakia_duality wikiPageWikiLink Functorial.
- Esakia_duality wikiPageWikiLink Heyting_algebra.
- Esakia_duality wikiPageWikiLink Homomorphism.
- Esakia_duality wikiPageWikiLink Homomorphisms.
- Esakia_duality wikiPageWikiLink Isomorphism.
- Esakia_duality wikiPageWikiLink Mathematics.
- Esakia_duality wikiPageWikiLink Prime_ideal.
- Esakia_duality wikiPageWikiLink Up-set.
- Esakia_duality wikiPageWikiLink Upper_set.
- Esakia_duality wikiPageWikiLinkText "Esakia duality".
- Esakia_duality hasPhotoCollection Esakia_duality.
- Esakia_duality wikiPageUsesTemplate Template:Citation_style.
- Esakia_duality wikiPageUsesTemplate Template:Math.
- Esakia_duality wikiPageUsesTemplate Template:Reflist.
- Esakia_duality subject Category:Lattice_theory.
- Esakia_duality subject Category:Topology.
- Esakia_duality hypernym Equivalence.
- Esakia_duality type Article.
- Esakia_duality type Scientist.
- Esakia_duality type Article.
- Esakia_duality type Field.
- Esakia_duality comment "In mathematics, Esakia duality is the dual equivalence between the category of Heyting algebras and the category of Esakia spaces. Esakia duality provides an order-topological representation of Heyting algebras via Esakia spaces.Let Esa denote the category of Esakia spaces and Esakia morphisms.Let H be a Heyting algebra, X denote the set of prime filters of H, and ≤ denote set-theoretic inclusion on the prime filters of H.".
- Esakia_duality label "Esakia duality".
- Esakia_duality sameAs ثنائية_إيزاكيا.
- Esakia_duality sameAs m.0bh6zlm.
- Esakia_duality sameAs Q5396694.
- Esakia_duality sameAs Q5396694.
- Esakia_duality wasDerivedFrom Esakia_duality?oldid=568479643.
- Esakia_duality isPrimaryTopicOf Esakia_duality.