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Let $(X,\tau)$ be a Hausdorff space. Which of the following statements MUST be true?

Select ALL that apply.

$\tau$ is the metric topology induced by some metric.

For every distinct $x,y\in X$, there exist disjoint open sets $U$ and $V$ with $x\in U$ and $y\in V$.

For every $x\in X$, $\{x\}$ is a closed set.

For every distinct closed sets $A$ and $B$, there exist distjoint open sets $U$ and $V$ with $A\subseteq U$ and $B\subseteq V$.

$\tau$ is the discrete topology.