(2)

Since is continuous on A it has a min., let we have (1)

By definition for all there is a natural number such that if we have: for all

Now divide by : by (1)

So by definition converges uniformly to on A

(3)

(a) Suppose converges uniformly to on a interval A and converges uniformly to also on A

By definition for all there is a natural number such that if we have: for all

Again for all there is a natural number such that if we have: for all

Set

Then for all there is a natural number such that if we have: and for all

Summing for all

Thus (definition) we have that converges uniformly to on A