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This paper gives an answer to Weihrauch's question [31] whether and, if not always, when an effective map between the computable elements of two represented sets can be extended to a (partial) computable map between the represented sets. Examples are known showing that this is not possible in general. A condition is introduced and for countably based(More)
In examples like the total recursive functions or the computable real numbers the canonical indexings are only partial maps. It is even impossible in these cases to nd an equivalent total numbering. We consider eeectively given topological T0-spaces and study the problem in which cases the canonical numberings of such spaces can be totalized, i. e., have an(More)
In programming language semantics different kinds of semantical domains are used, among them Scott domains and metric spaces. D. Scott raised the problem of finding a suitable class of spac~ which should include Scott domains and metric spaces such that effective mappings between these spaces are continuous. It is well known that between spaces like(More)