Admissible Representations in Computable Analysis

  • Matthias Schröder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

Computable Analysis investigates computability on real numbers and related spaces. One approach to Computable Analysis is Type Two Theory of Effectivity (TTE). TTE provides a computational framework for non-discrete spaces with cardinality of the continuum. Its basic tool are representations. A representation equips the objects of a given space with “names”, which are infinite words. Computations are performed on these names.

We discuss the property of admissibility as a well-behavedness criterion for representations. Moreover we investigate and characterise the class of spaces which have such an admissible representation. This category turns out to have a remarkably rich structure.

Keywords

Computable Analysis TTE Admissibility Topological Spaces Cartesian-Closed Categories 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthias Schröder
    • 1
  1. 1.LFCS, School of InformaticsUniversity of EdinburghEdinburghUK

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