Absolutely non-effective predicates and functions in computable analysis

Authors:
Decheng Ding;Klaus Weihrauch;Yongcheng Wu
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, China;Department of Mathematics and Computer Science, University of Hagen, Germany;Nanjing University of Information Science and Technology, Nanjing, China
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

Citing 3
Cited 1

Computability on computable metric spaces

Theoretical Computer Science
Computable analysis: an introduction

Computable analysis: an introduction
A computable version of the Daniell-Stone theorem on integration and linear functionals

Theoretical Computer Science

Absolutely non-computable predicates and functions in analysis†

Mathematical Structures in Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the representation approach (TTE) to Computable Analysis those representations of an algebraic or topological structure are of interest, for which the basic predicates and functions become computable. There are, however, natural examples of predicates and functions, which are not computable, even not continuous, for any representations. All these results follow from a simple lemma. In this article we prove this lemma and apply it to a number of examples. In particular we prove that various predicates and functions on computable measure spaces are not continuous for any representations, that means "absolutely non-effective".