Resumen de Topo-canonical completions of closure algebras and Heyting algebras

Guram Bezhanishvili, Ray Mines, Patrick J. Morandi

• 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.