Computable analysis: an introduction
Computable analysis: an introduction
On Computable Metric Spaces Tietze-Urysohn Extension Is Computable
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Borel Complexity of Topological Operations on Computable Metric Spaces
Journal of Logic and Computation
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We investigate some basic connections between reverse mathematics and computable analysis. In particular, we show how to use Weak Konig's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and through the definition of a natural notion of reducibility for multi-valued functions, we obtain a computational counterpart of the subsystem of second order arithmetic WKL"0. We study analogies and differences between WKL"0 and the class of Sep-computable multi-valued functions. We use these notions to provide a method to determine the computational complexity of the Hahn-Banach Extension Theorem.