Hi
Q3: Define the space c and prove that the space is a subspace of X and c is closed in X. Then prove that c is complete. (12 marks)
Q4: If d is a metric on a vector space X, where X is obtained from a norm, and d is defined by d(x,x)=0 and d(x,y)=d(x,y)+1, show that d cannot be obtained from a norm. (12 marks)