Source: wikibot/heine-borel-theorem
= Heine–Borel theorem
{wiki=Heine–Borel_theorem}
The Heine–Borel theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space. The theorem states that in \\(\\mathbb\{R\}^n\\), a subset is compact if and only if it is closed and bounded. To elaborate: 1. **Compact Set**: A set \\( K \\) is compact if every open cover of \\( K \\) has a finite subcover.