Invariance of domain
Invarianza del dominio
- Date
- 1912 · confidence high
- Place
- Amsterdam, Netherlands
- Credited to
- Proved by L. E. J. Brouwer in 1912, as an application of his algebraic topology techniques (mapping degree).
- Field
- Knowledge & symbols
What was discovered
Topology theorem stating that if an open subset of Rⁿ is mapped injectively and continuously into Rⁿ, its image is also open; a far from trivial result despite its intuitive appearance.
What it led to
- Establishment of algebraic topology as a rigorous tool
- Foundation for proving Rᵐ and Rⁿ are not homeomorphic when m≠n
- Applications in manifold theory