Editing Heine–Borel theorem (section)

{{short description|Subset of Euclidean space is compact if and only if it is closed and bounded}}
In [[real analysis]], the '''Heine–Borel theorem''', named after [[Eduard Heine]] and [[Émile Borel]], states:

For a [[subset]] <math>S</math> of [[Euclidean space]] <math>\mathbb{R}^n</math>, the following two statements are equivalent:
*<math>S</math> is [[compact space#Open cover definition|compact]], that is, every open [[cover (topology)|cover]] of <math>S</math> has a finite subcover
*<math>S</math> is [[closed set|closed]] and [[bounded set|bounded]].