Dieter Spreen

Learn More
Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological To-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that(More)
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)
If one wants to compute with infinite objects like real numbers or data streams, continuity is a necessary requirement: better and better (finite) approximations of the input are transformed in better and better (finite) approximations of the output. In case the objects are constructively generated, they can be represented by a finite description of the(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)