Prove the separation theorem, Theorem 4.3.6. Hints. For the first statement, reduce the general case to the problem of separating A − B = {a − b | a ∈ A, b ∈ B} from the origin if 0 ∈ A − B. Note that...

Prove the separation theorem, Theorem 4.3.6.

Hints. For the first statement, reduce the general case to the problem of

separating A − B = {a − b | a ∈ A, b ∈ B} from the origin if 0 ∈ A − B.

Note that we have already established this fact. For the second statement, show

that A − B is closed if A is closed and B is compact.