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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.

MSC:
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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