ABSTRACT
Proposition 5.1 Let S ⊆ RN be any set. Then the polar So of S is convex. Also the polar contains the origin.
Proof: The second assertion is obvious. For the first, let α1, α2 ∈ So. Then, for 0 ≤ t ≤ 1 and x ∈ S,[
(1− t)α1 + tα2 ] · x = (1− t)[α1 · x]+ t[α2 · x]
≤ (1− t) · 1 + t · 1 = 1 .
