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We consider the problem of extending maps from algebras to their profinitecompletions in finitely generated quasivarieties. Our developments are based onthe construction of the profinite completion of an algebra as its naturalextension. We provide an extension which is a multi-map and we study itscontinuity properties, and the conditions under which it is a map.

Extending maps to profinite completions in finitely generated quasivarieties