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Theory of Computing Systems

, Volume 50, Issue 2, pp 370–386 | Cite as

Computing Space-Filling Curves

  • P. J. Couch
  • B. D. Daniel
  • Timothy H. McNicholl
Article

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.

Keywords

Computable analysis Constructive analysis Peano continua Space-filling curves Locally connected spaces 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • P. J. Couch
    • 1
  • B. D. Daniel
    • 2
  • Timothy H. McNicholl
    • 2
  1. 1.Department of MathematicsAuburn UniversityAuburnUSA
  2. 2.Department of MathematicsLamar UniversityBeaumontUSA

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