Computability on metric spaces

Weihrauch, Klaus

It is shown that certain effective metric spaces can be reasonably embedded into (weakly) effective algebraic cpo's. The construction is similar to that one given by Lacombe, it is, however, more effective. Computability of points and of functions for the metric spaces can be naturally derived from computability for effective cpo's, for which a nice theory already exists. A generalized version of a theorem of Kreisel / Lacombe / Shoenfield can be proved in this framework.

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Weihrauch, Klaus: Computability on metric spaces. Hagen 1981. FernUniversität in Hagen.

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