Continuity and Computability of Relations
The main theorem of the theory of effectivity ( cf. Kreitz and Weihrauch [KWl], [Wl]) states that in admissibly represented topological spaces a function is continuous iff it has a continuous representation. Hence continuity is a necessary condition for computability. We investigate an extended model of computability in order to compute relations. From another point of view these relations are nondeterministic operations or set-valued functions. We show that for a special class of topological spaces (including the complete separable metric ones) and for a certain notion of continuity for relations the main theorem can be extended too.
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