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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 be a Heyting algebra, denote the set of prime filters of , and denote set-theoretic inclusion on the prime filters of . Also, for each , let , and let denote the topology on generated by }. Theorem:〔Esakia (1974).〕 is an Esakia space, called the ''Esakia dual'' of . Moreover, is a Heyting algebra isomorphism from onto the Heyting algebra of all clopen up-sets of . 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:〔Esakia (1974), Esakia (1985), Bezhanishvili (2006).〕 HA is dually equivalent to Esa. ==Notes== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Esakia duality」の詳細全文を読む スポンサード リンク
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