Pick out the true statement(s).
(a) If $f :(−1, 1)\to\Bbb R$ is bounded and continuous, it is uniformly continuous.
(b) If $f : S^1\to\Bbb R$ is continuous, it is uniformly continuous.
(c) If $(X, d)$ is a metric space and $A\subseteq X$, then the function $f(x) = d(x,A)$ defined by $d(x,A) = \inf\{d(x, y) : y \in A\}$ is uniformly continuous.
i think a is false as domain is not closed and b is true as domain is closed and bounded. no idea about c