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November 26th, 2010, 08:42 AM   #1
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Convex hull

Hello all,
Here is question seemingly obvious but I can't find the answer:

Let E a set of n points (X1,,Xn) in the d-dimensional euclidian space ; Xi=(x1,i,,xd,i). Let us denote by CH(X) the convex hull of (X1,,Xn). Let f1, f2,.,fd a collection of real-valued functions continuous, strictly increasing and smooth, such that Yi=(f1(x1,i),,fd(xd,i)). Let us denote by CH(Y) the convex hull of (Y1,,Yn).

my question is:

How to show that a new point Xn+1 belongs to CH(X) if and only if Yn+1 belongs to CH(Y).

thanks in advance
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