linguistic:voice_change
Euclidean space

For any subset A of Euclidean space, A is compact if and only if it is closed and bounded; this is the Heine–Borel theorem.

As a Euclidean space is a metric space, the conditions in the next subsection also apply to all of its subsets. Of all of the equivalent conditions, it is in practice easiest to verify that a subset is closed and bounded, for example, for a closed interval or closed n -ball.