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Two point set extensions- a counterexample

Author(s): Jan J. Dijkstra; Jan van Mill
Journal: Proc. Amer. Math. Soc. 125 (1997), 2501-2502.
MSC (1991): Primary 54G20
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Abstract: We show that there exist Cantor sets in the circle that are not extendable to sets that meet every line in the plane in exactly two points. This result solves a problem that was formulated by R. D. Mauldin.

References:

1.: R. D. Mauldin, Problems in topology arising from analysis, Open Problems in Topology, J. van Mill and G. M. Reed, eds., North-Holland, Amsterdam, 1990, pp. 617-629. CMP 91:03
2.: R. D. Mauldin, On sets which meet each line in exactly two points, in preparation.
3.: J. van Mill and G. M. Reed, Open problems in topology, Topology Appl. 62 (1995), 93-99. MR 95m:54001

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Additional Information:

Jan J. Dijkstra
Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
Email: jdijkstr@ua1vm.ua.edu

Jan van Mill
Affiliation: Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Email: vanmill@cs.vu.nl

DOI: 10.1090/S0002-9939-97-03875-6
PII: S 0002-9939(97)03875-6
Received by editor(s): June 17, 1995
Received by editor(s) in revised form: February 29, 1996
Additional Notes: The first author is pleased to thank the Vrije Universiteit in Amsterdam for its hospitality and support.
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1997, American Mathematical Society


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