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

 

Every three-point set is zero dimensional


Authors: David L. Fearnley, L. Fearnley and J. W. Lamoreaux
Journal: Proc. Amer. Math. Soc. 131 (2003), 2241-2245
MSC (2000): Primary 54B05, 54H05, 54F45
Published electronically: January 28, 2003
MathSciNet review: 1963773
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Abstract: This paper answers a question of Jan J. Dijkstra by giving a proof that all three-point sets are zero dimensional. It is known that all two-point sets are zero dimensional, and it is known that for all $n > 3$, there are $n$-point sets which are not zero dimensional, so this paper answers the question for the last remaining case.


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Additional Information

David L. Fearnley
Affiliation: Department of Mathematics, Utah Valley State College, Orem, Utah 84058
Email: davidfearnley@juno.com

L. Fearnley
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602

J. W. Lamoreaux
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: jack@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06432-3
PII: S 0002-9939(03)06432-3
Keywords: $n$-point set, zero dimensonal
Received by editor(s): September 7, 2000
Received by editor(s) in revised form: April 27, 2001
Published electronically: January 28, 2003
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society