when quoting this document, please refer to the following
DOI: 10.4230/OASIcs.CCA.2009.2264
URN: urn:nbn:de:0030-drops-22649
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2264/

de Brecht, Matthew ; Yamamoto, Akihiro
Contributed Papers

Sigma^0_alpha - Admissible Representations (Extended Abstract)

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Abstract

We investigate a hierarchy of representations of topological spaces by measurable functions that extends the traditional notion of admissible representations common to computable analysis. Specific instances of these representations already occur in the literature (for example, the naive Cauchy representation of the reals and the jump'' of a representation), and have been used in investigating the computational properties of discontinuous functions. Our main contribution is the integration of a recently developing descriptive set theory for non-metrizable spaces that allows many previous results to generalize to arbitrary countably based $T_0$ topological spaces. In addition, for a class of topological spaces that include the reals (with the Euclidean topology) and the power set of $\omega$ (with the Scott-topology), we give a complete characterization of the functions that are (topologically) realizable with respect to the level of the representations of the domain and codomain spaces.

BibTeX - Entry

@InProceedings{debrecht_et_al:DSP:2009:2264,
author =	{Matthew de Brecht and Akihiro Yamamoto},
title =	{Sigma^0_alpha - Admissible Representations (Extended Abstract)},
booktitle =	{6th Int'l Conf. on Computability and Complexity in Analysis},
year =	{2009},
editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},