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Computing Space-Filling Curves

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Abstract

We show that a continuous surjection of [0,1] onto a Euclidean Peano continuum X can be computed uniformly from a name of X as a compact set and a local connectivity operator for X. We show by means of an example that the second parameter is not superfluous. We then show that this parameter is not necessary either in that there is a computable map of [0,1] into ℝ2 whose image is not effectively locally connected.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, Auburn, AL, 36849, USA

    P. J. Couch

  2. Department of Mathematics, Lamar University, Beaumont, TX, 77710, USA

    B. D. Daniel & Timothy H. McNicholl

Authors
  1. P. J. Couch
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  2. B. D. Daniel
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  3. Timothy H. McNicholl
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Correspondence to Timothy H. McNicholl.

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Couch, P.J., Daniel, B.D. & McNicholl, T.H. Computing Space-Filling Curves. Theory Comput Syst 50, 370–386 (2012). https://doi.org/10.1007/s00224-010-9306-3

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  • DOI: https://doi.org/10.1007/s00224-010-9306-3

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