Which of the following statements regarding compact metric spaces $(X, d)$ is/are TRUE according to real analysis?
(A)
Every continuous function $f: X \to \mathbb{R}$ on a compact metric space is bounded and attains its extrema
(B)
Every continuous function $f: X \to \mathbb{R}$ on a compact metric space is uniformly continuous
(C)
Every infinite subset of a compact metric space has a limit point in $X$
(D)
Every open cover of $X$ contains a finite subcover only if $X$ is a finite set