November 26th, 2010, 08:42 AM  #1 
Newbie Joined: Nov 2010 Posts: 1 Thanks: 0  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 ddimensional 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 realvalued 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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