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Selected Works of Timothy McNicholl
Article
Computing Space-Filling Curves
Theory of Computing Systems (2012)
  • P. J. Couch, Auburn University
  • B. D. Daniel, Lamar University
  • Timothy H. McNicholl, Lamar University
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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.
Keywords
  • Computable analysis,
  • Constructive analysis,
  • Peano continua,
  • Space-filling curves,
  • Locally connected spaces
Disciplines
Publication Date
2012
DOI
10.1007/s00224-010-9306-3
Publisher Statement
The final publication is available at Springer via https://doi.org/10.1007/s00224-010-9306-3.
Copyright 2010, Springer Science+Business Media, LLC
Citation Information
P. J. Couch, B. D. Daniel and Timothy H. McNicholl. "Computing Space-Filling Curves" Theory of Computing Systems Vol. 50 Iss. 2 (2012) p. 370 - 386
Available at: http://works.bepress.com/timothy-mcnicholl/5/