Brouwer fixed-point theorem
Teorema del punto fijo de Brouwer
- Date
- 1911 · confidence high
- Place
- Amsterdam, Netherlands
- Credited to
- L. E. J. Brouwer
- People
- 👤 Luitzen Egbertus Jan Brouwer1881–1966
- Field
- Knowledge & symbols
What was discovered
Every continuous map from a closed ball to itself has a fixed point; Brouwer also proved the invariance of dimension. A central tool for proving the existence of equilibria and solutions.
Brouwer, the founder of intuitionism, ended up rejecting non-constructive proofs such as that of his own theorem.
What it led to
- Kakutani's theorem
- Nash equilibrium
- general equilibrium (Arrow-Debreu)
- algebraic topology
Built on
- Poincaré's Analysis Situs
- Hadamard