9. For 1a pay, define a set, GHR2 to be ‘‘lp-open’’ if for any x A G there is an r > 0 so that BðpÞ r ðxÞHG where BðpÞ r ðxÞ ¼ fy j kx  ykp < rg, and where kx  ykp denotes the lp-norm. The usual definition of open is then l2-open.

(a) Show that G is open if and only if it is l1-open. (Hint: Recall the graphs of equivalent metrics in chapter 3.)

(b) Generalize part

(a) to show that G is open if and only if it is lp-open for all p.