a. Show that the set of all rectangles [a1, b1] x . x [an, bn] where each

Question:

a. Show that the set of all rectangles [a1, b1] x . x [an, bn] where each ai and each bi are rational can be arranged into a sequence (i.e. form a countable set).
b. If A C Rn is any set and O is an open cover of A, show that there is a sequence U1, U2, U3,. of members of O which also cover A.