Let $f\colon S\to\Bbb R$ be uniformly continuous. Let $A\subset S$. Show that the restriction $f\mid _A$ is uniformly continuous.
I have the following:
There exists an $\alpha > 0$ such that
$(a-\alpha,a+\alpha)/\{a\}$ intersected with $A=(a-\alpha,a+\alpha)/\{a\}$ intersected with S.
Since f[a is within f, all points in f[a are in f this if f is uniformly continuous then f[a is as well.
Is this enough, if not I am not sure which direction to take.