Question 2: Let V be an F vector space, || || and || ||' two norms on V. For each & > 0 and a V. Let B(x, e) and B'(x, e) denotes the e-open ball at in (V, ||-|| and (V,||||') respectively. Show that a) ||-|| and || ||' are equivalent B'(0, 1) C B(0,r) and B(0, 1) C B'(0, R) for some r, R>0 b) Use a) to show that Equivalent norms generate the same topology on V. c) |||| and || ||' are equivalent the identity map I: (V||||) (V ||||') is a Homeomorphism. [10,6,10] Question 3: Let a R-{0}. Show that the space C[-a, a] of all real-valued continuous functions on [-a, a], with the norm ||||2 = ( ["* x(t)dt)}/ is not a Banach space. [10]