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Proceedings of the American Mathematical Society

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Two point set extensions-
a counterexample


Authors: Jan J. Dijkstra and Jan van Mill
Journal: Proc. Amer. Math. Soc. 125 (1997), 2501-2502
MSC (1991): Primary 54G20
DOI: https://doi.org/10.1090/S0002-9939-97-03875-6
MathSciNet review: 1396973
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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), no. 1, 93–99. MR 1318431, https://doi.org/10.1016/0166-8641(94)00092-H

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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: https://doi.org/10.1090/S0002-9939-97-03875-6
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
Article copyright: © Copyright 1997 American Mathematical Society