Dieter Spreen

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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 this paper a new notion of continuous information system is introduced. It is shown that the information systems of this kind generate exactly the continuous domains. The new information systems are of the same logic-oriented style as the information systems first introduced by Scott in 1982: they consist of a set of tokens, a consistency predicate and(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 this paper o-algebraic complete partial orders are considered the compact elements of which are not maximal in the partial order. Under the assumption that these elements are indexed such that their equality is decidable and the order is semi-decidable (completely enumerable) it is shown that the computable domain elements can be effectively enumerated(More)