Abstract.
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.
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Received January 20, 2006; accepted in final form September 12, 2006.
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Bezhanishvili, G., Mines, R. & Morandi, P.J. Topo-canonical completions of closure algebras and Heyting algebras. Algebra univers. 58, 1–34 (2008). https://doi.org/10.1007/s00012-007-2032-2
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DOI: https://doi.org/10.1007/s00012-007-2032-2