21 19 [6] Let (X,) be a normed space and A a non-empty. For any x = X, we set == dA(x) = d(x, A) inf{||xa||, a A} 3-1. Show that d is well define i.e. the infimum exists. 3-2. Assume A is closed and show that VxEX, d(x)=0xA 3-3. Assume X = C([0, 1]) equipped with the norm ||f|| = supre(0,1)|f(x)|. We consider the set A={fe X f(0) = 0 and 3-3-1. Show that A is closed. 3-3-2. Show that d(0) > 1. 3-3-3. Consider the sequence f(x): to show that d(0) 1. Conclude. : [f(t)dt > 1} [(n+1)x, if 0 x 1+ 1, if x1