If is a bounded set, then there exists a sequence of functions from to that is uniform convergent but not pointwise convergent.

Any sequence of polynomial functions which is pointwise convergent is also uniform convergent.

Any sequence of constant functions which is pointwise convergent is also uniform convergent.

If is a finite set, then any sequence of functions from to that is pointwise convergent is also uniform convergent.

If is a bounded set, then any sequence of functions from to that is pointwise convergent is also uniform convergent.