Editing Compact space (section)

==== Euclidean space ====

For any [[subset]] {{mvar|A}} of [[Euclidean space]], {{mvar|A}} is compact if and only if it is [[closed set|closed]] and [[bounded set|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 (mathematics)|interval]] or closed {{mvar|n}}-ball.