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There are no n-point Fσ sets in Rm
Published online by Cambridge University Press: 17 April 2009
Extract
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
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