Algebra the questions is from functional analysis by balmohan limaye. (Q10 and 11 section 5) 5-10 Let X be a closed subspace and X2 be a finite dimensional subspace of a normed space X. Then X + X2 is closed in X. (Hint: Proof of 5.4(b)). 5-11 Let X be a normed space such that U(0, 1) is totally bounded. Then X is finite dimensional. (Hint: Proof of '(ii) implies (iii)' of Theorem 5.5) please prove both