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International Workshop on Computability and Complexity in Analysis

CCA 2000: Computability and Complexity in Analysis pp 69–81Cite as

Banach-Mazur Computable Functions on Metric Spaces

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2064))

Abstract

We present Mazur’s continuity results for Banach-Mazur computable functions on computable real numbers in the slightly more general setting of metric spaces satisfying suitable computability conditions. Additionally, we prove that the image of a computable, computably convergent sequence under a Banach-Mazur computable function is again computably convergent.

Acknowledgements

I would like to thank Vasco Brattka and Klaus Weihrauch for interesting discussions on topics related to this paper, and Jeffery Zucker for valuable comments on an earlier version of the paper.

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References

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Author information

Authors and Affiliations

  1. Theoretische Informatik I, FernUniversität Hagen, 58084, Hagen, Germany

    Peter Hertling

Authors
  1. Peter Hertling
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Editor information

Editors and Affiliations

  1. University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK

    Jens Blanck

  2. Informatikzentrum, FernUniversität Hagen, 58084, Hagen, Germany

    Vasco Brattka  & Peter Hertling  & 

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Hertling, P. (2001). Banach-Mazur Computable Functions on Metric Spaces. In: Blanck, J., Brattka, V., Hertling, P. (eds) Computability and Complexity in Analysis. CCA 2000. Lecture Notes in Computer Science, vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45335-0_5

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  • DOI: https://doi.org/10.1007/3-540-45335-0_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42197-9

  • Online ISBN: 978-3-540-45335-2

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