Find two closed convex sets such that Corollary 7.3 fails. 7.3. In E3, consider the close d convex set (cone) A defined by the inequalities   And let D be the line given by x = 0 ,z =1. Prove that D∩A...

Find two closed convex sets such that Corollary 7.3 fails. 7.3. In

E3, consider the close d convex set (cone) A defined by the inequalities

And let D be the line given by x = 0 ,z =1. Prove that D∩A =/0, both A and D are convex and closed, yet every plane containing D meets A. Therefore, A and D give an other counter example to the Hahn–Banach the o rem in which A is closed (one can not relax the hypo thesis that A is open).