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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

No $n$-point set is $\sigma$-compact


Authors: Khalid Bouhjar, Jan J. Dijkstra and R. Daniel Mauldin
Journal: Proc. Amer. Math. Soc. 129 (2001), 621-622
MSC (2000): Primary 54H05, 57N05, 54G99
Published electronically: September 27, 2000
MathSciNet review: 1800242
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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.


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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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05869-X
PII: S 0002-9939(00)05869-X
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
Article copyright: © Copyright 2000 American Mathematical Society