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- Andrej Bauer, Dana S. Scott, Steven M. Awodey, Lenore Blum, Abbas Edalat, Frank Pfenning +51 others
- 2000

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)

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)

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)