Notice: • All the assignments must be submitted before the deadline. • Each assignment should include your name and student ID number. 1. Show that kxk = Xn k=0 sup t∈[0,1] |x (k) (t)| (1) is a norm on C n [0, 1]. 2. Let K be a compact topological space. Prove that the spaces C(K) with sup-norm and C n [0, 1] with the norm defined in (1) are Banach spaces. — THE END — 1
