Heine–Borel theorem
Teorema de Heine-Borel
- Date
- 1895 · confidence medium
- Place
- Paris, France
- Credited to
- Émile Borel (building on earlier work by Eduard Heine)
- Field
- Knowledge & symbols
What was discovered
A theorem of real analysis stating that, in Euclidean space, a subset is compact if and only if it is closed and bounded; a fundamental tool of modern analysis.
Also called the Borel–Lebesgue lemma; Lebesgue contributed to its modern form.
What it led to
- Modern formalization of the concept of compactness
- Basis for later results in analysis and topology