Computability on computable metric spaces
Theoretical Computer Science
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Theoretical Computer Science - Special issue on computability and complexity in analysis
Effective properties of sets and functions in metric spaces with computability structure
Theoretical Computer Science - Special issue on computability and complexity in analysis
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Computability theory of generalized functions
Journal of the ACM (JACM)
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Continuity and computability of reachable sets
Theoretical Computer Science
A computable version of dini's theorem for topological spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
Electronic Notes in Theoretical Computer Science (ENTCS)
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In this paper we investigate aspects of effectivity and computability on partial continuous functions in topological spaces. We use the framework of TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We generalize the representations introduced in [Weihrauch, K., ''Computable Analysis,'' Springer, Berlin, 2000] for the Euclidean case to computable T"0-spaces and computably locally compact Hausdorff spaces respectively. We show their equivalence and in particular, prove an effective version of the Stone-Weierstrass approximation theorem.