Bull. Austral. Math. Soc. 72(3) pp.477--480, 2005.

There are no n-point F_σ sets in R^m

David L. Fearnley

L. Fearnley

J.W. Lamoreaux

Received: 29th August, 2005

Abstract

We show that, for any positive integers n and m, if a set S $\subset$ R^m intersects every m - 1 dimensional affine hyperplane in R^m in exactly n points, then S is not an F 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.

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MathSciNet: MR2199649

Z'blatt-MATH: 1091.54003

References

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ISSN 0004-9727

Bulletin of the Australian Mathematical Society

There are no n-point Fσ sets in Rm