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From: Maury Barbato on 7 Aug 2010 01:47
Hello,
let C be a convex set in R^n, with non-empty interior,
and p a point in the boundary of C. Does there exist
a supporting hyperplen H to C in p and an open
neighborhood N of p such that for every x in H /\ N
there's exactly one point q in N /\ Bd(C) on the
straight line passing through X and orthogonal to H?
If this were true, the boundary of a convex set would
be, locally, the graph of a convex function.

Thank you very very much for your help.
My Best Regards,
Maury Barbato
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