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Every three-point set is zero dimensional

Author(s): David L. Fearnley; L. Fearnley; J. W. Lamoreaux
Journal: Proc. Amer. Math. Soc. 131 (2003), 2241-2245.
MSC (2000): Primary 54B05, 54H05, 54F45
Posted: January 28, 2003
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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 , there are -point sets which are not zero dimensional, so this paper answers the question for the last remaining case.

References:

1.: Jan J. Dijkstra, On -point sets, Topology and Dynamics Conference, San Antonio, Texas, 2000.
2.: Khalid Bouhjar, Jan J. Dijkstra, Jan Van Mill, Three point sets, Top. Appl., 112 (2001), 215-227. CMP 2001:10
3.: B. Engelking, Dimension theory, PWN, Warszawa, 1978. MR 58:2753b
4.: John Kulesza, A two point set must be zero dimensional, Proc. Amer. Math. Soc. 116 (1992), 551-553. MR 92m:54064
5.: R. D. Mauldin, Problems in topology, Open Problems in Topology, J. Van Mill and G. M. Reed, eds., North-Holland, Amsterdam, 1990. MR 92c:54001


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