Every three-point set is zero dimensional
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- by David L. Fearnley, L. Fearnley and J. W. Lamoreaux PDF
- Proc. Amer. Math. Soc. 131 (2003), 2241-2245 Request permission
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.References
- Jan J. Dijkstra, On $n$-point sets, Topology and Dynamics Conference, San Antonio, Texas, 2000.
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- John Kulesza, A two-point set must be zero-dimensional, Proc. Amer. Math. Soc. 116 (1992), no. 2, 551–553. MR 1093599, DOI 10.1090/S0002-9939-1992-1093599-1
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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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2241-2245
- MSC (2000): Primary 54B05, 54H05, 54F45
- DOI: https://doi.org/10.1090/S0002-9939-03-06432-3
- MathSciNet review: 1963773