No $n$-point set is $\sigma$-compact
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- by Khalid Bouhjar, Jan J. Dijkstra and R. Daniel Mauldin PDF
- Proc. Amer. Math. Soc. 129 (2001), 621-622 Request permission
Abstract:
Let $n$ be an integer greater than 1. We prove that there exist no $F_\sigma$-subsets of the plane that intersect every line in precisely $n$ points.References
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Additional Information
- Khalid Bouhjar
- Affiliation: Faculty of Sciences, Division of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081 A, 1081 HV Amsterdam, The Netherlands
- Email: kbouhjar@cs.vu.nl
- Jan J. Dijkstra
- Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
- MR Author ID: 58030
- Email: jdijkstr@obelix.math.ua.edu
- R. Daniel Mauldin
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: mauldin@dynamics.math.unt.edu
- Received by editor(s): November 30, 1999
- Received by editor(s) in revised form: January 7, 2000
- Published electronically: September 27, 2000
- Additional Notes: The second author was supported in part by a grant from the Research Advisory Committee of the University of Alabama.
The third author was supported in part by NSF grant DMS-9801583. - Communicated by: Alan Dow
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 621-622
- MSC (2000): Primary 54H05, 57N05, 54G99
- DOI: https://doi.org/10.1090/S0002-9939-00-05869-X
- MathSciNet review: 1800242