Topo-canonical completions of closure algebras and Heyting algebras

• Autores: Guram Bezhanishvili, Ray Mines, Patrick J. Morandi
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 58, Nº. 1, 2008, págs. 1-34
• Idioma: inglés
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• Resumen

  • We introduce and investigate topo-canonical completions of closure algebras and Heyting algebras. We develop a duality theory that is an alternative to Esakia�s duality, describe duals of topo-canonical completions in terms of the Salbany and Banaschewski compactifications, and characterize topo-canonical varieties of closure algebras and Heyting algebras. Consequently, we show that ideal completions preserve no identities of Heyting algebras. We also characterize definable classes of topological spaces.