1. Show that the Cantor set A contains no (non-empty) open interval. (Hint: Show that if x, y E A with then there exists some z E [0,1] \ A so that x x. (b) For each subset A of M: A is open in (M, d) if and only if it is open in (M, p). 3. Let 1 0, the set Ajr: = {x = (xn) Elp: |x;|