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Topo-canonical completions of closure algebras and Heyting algebras. (English) Zbl 1135.06009
In this long paper there is introduced the notion of topo-canonical completions of closure algebras and Heyting algebras. The connection with canonical completions is exhibited by showing that the McKinsey-Tarski topology, which gives rise to the topo-canonical completion, is the intersection of the Stone topology and the Alexandroff topology, the latter of which gives rise to the canonical completion. The duals of topo-canonical completions are described in terms of the Salbany and Banaschewski compactifications, and topo-canonical varieties are characterised. In particular there is established the interesting fact that topo-canonical completions of Heyting algebras, which are isomorphic to their ideal completions, preserve no identities of Heyting algebras.

06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
06D20 Heyting algebras (lattice-theoretic aspects)
06E15 Stone spaces (Boolean spaces) and related structures
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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