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12. Let V, W, X be normed vector spaces and let A:V→W and C:W→X be bounded linear operators. Show that:

||CA||B(V,W) ≤ ||C||B(w,x)||A||B(v,W)

13. Show that if ||·|| is a norm on Rn, a ∈ Rn, r > 0, then the open ||·|| ball of radius r centered at a, B(a,r, ||·||) is itself an open subset of Rn.