Baire category theorem
Teorema de categorías de Baire
- Date
- 1899 · confidence high
- Place
- Paris, France
- Credited to
- René-Louis Baire
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A central result of general topology and functional analysis giving sufficient conditions for a topological space to be a Baire space, meaning the intersection of countably many dense open sets is still dense.
Osgood proved it independently in 1897 for the real line; Baire proved it in 1899 for Euclidean space.
What it led to
- Proofs of fundamental theorems of functional analysis
- Generalization to completely metrizable spaces by Hausdorff in 1914