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There are no n-point Fσ sets in Rm

Published online by Cambridge University Press:  17 April 2009

David L. Fearnley ,
L. Fearnley  and
J. W. Lamoreaux
David L. Fearnley
Affiliation:
Department of Mathematics, Utah Valley State College, Orem, UT., United States of America, e-Mail: dfearnley@Math.byu.edu
L. Fearnley
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT., United States of America, e-mail: fearnlda@uvsc.edu
J. W. Lamoreaux
Affiliation:
Department of Mathematics, Utah Valley State College, Orem, UT., United States of America, e-Mail: dfearnley@Math.byu.edu
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We show that, for any positive integers n and m, if a set S ⊂ Rm intersects every m − 1 dimensional affine hyperplane in Rm in exactly n points, then S is not an Fσ set. This gives a natural extension to results of Khalid Bouhjar, Jan J. Dijkstra, and R. Daniel Mauldin, who have proven this result for the case when m = 2, and also Jan J. Dijkstra and Jan van Mill, who have shown this result for the case when n = m.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 477 - 480
Copyright
Copyright © Australian Mathematical Society 2005

References

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