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# Let S be a convex set in En and S a convex set in Em. Suppose T is an m n matrix that establishes a one-to-one correspondence between S and S , i.

Let S be a convex set in En and S ∗ a convex set in Em. Suppose T is an m × n

matrix that establishes a one-to-one correspondence between S and S ∗, i.e., for

every s ∈ S there is s∗ ∈ S ∗ such that Ts = s∗, and for every s∗ ∈ S ∗ there is a

single s ∈ S such that Ts = s∗. Show that there is a one-to-one correspondence

between extreme points of S and S ∗.