## EnglishEdit

### EtymologyEdit

Named after the German *Eduard Heine* (1821–1881) and the French *Émile Borel* (1871–1956).

### NounEdit

**Heine–Borel theorem** (*uncountable*)

- (analysis) A theorem which states that for any subset
*S*of an*n*-dimensional Euclidean space,*S*is compact if and only if it is both closed and bounded.