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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The power of backtracking and the confinement of length


Author: Timothy H. McNicholl
Journal: Proc. Amer. Math. Soc. 141 (2013), 1041-1053
MSC (2010): Primary 03F60, 03D32, 54D05
Published electronically: August 7, 2012
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Abstract: We show that there is a point on a computable arc that does not belong to any computable rectifiable curve. We also show that there is a point on a computable rectifiable curve with computable length that does not belong to any computable arc.


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Additional Information

Timothy H. McNicholl
Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710
Address at time of publication: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: McNichol@iastate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11385-1
PII: S 0002-9939(2012)11385-1
Received by editor(s): April 5, 2011
Received by editor(s) in revised form: August 2, 2011, and August 4, 2011
Published electronically: August 7, 2012
Communicated by: Julia Knight
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.