@article {FeFeLa2005,
 author="David L. Fearnley, L. Fearnley and J.W. Lamoreaux",
 title={There are no $n$-point $F_\sigma $ sets in $R^m$},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="3",
 pages="477--480",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="29th August, 2005",
 classmath="54B05, 54H05, 54F45",
 publisher={AMPAI, Australian Mathematical Society},
 url="http://www.austms.org.au/Publ/Bulletin/V72P3/723-5241-FeFeLa/index.shtml",
 acknowledgement={},
 abstract={ \par 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 $F_{\sigma }$ 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 $n=m$. \par }
}