Let (X,d) be a metric space and A,B $\subset$ X be two compact subsets. Show $A\cap B$ is also compact.
I attempted this question by showing the intersection is bounded and closed.
But I stated that Bounded and Closed $\Rightarrow$ Compact (Heine-Borel) but I didn't realise this only holds for $\mathbb R^n$.
Most of the other similar problems on here were dealing with $\mathbb R^n$, so how would you go about showing this for a general space X?
Any help would be greatly appreciated!