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Effective Dispersion in Computable Metric Spaces

Author Zvonko Iljazovic

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OASIcs.CCA.2009.2268.pdf
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Keywords
  • Computable metric space
  • effective separating sequence
  • computability structure
  • effectively totally bounded computable metric space
  • effectively disp

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Abstract

We investigate the relationship between computable metric spaces $(X,d,\alpha )$ and $(X,d,\beta ),$ where $(X,d)$ is a given metric space. In the case of Euclidean space, $\alpha $ and $\beta $ are equivalent up to isometry, which does not hold in general. We introduce the notion of effectively dispersed metric space. This notion is essential in the proof of the main result of this paper: $(X,d,\alpha )$ is effectively totally bounded if and only if $(X,d,\beta )$ is effectively totally bounded, i.e. the property that a computable metric space is effectively totally bounded (and in particular effectively compact) depends only on the underlying metric space.

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Zvonko Iljazovic. Effective Dispersion in Computable Metric Spaces. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 161-172, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/OASIcs.CCA.2009.2268

Author Details

Zvonko Iljazovic
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