Continuous mappings | Homeomorphisms | Theorems in topology | Algebraic topology

Invariance of domain

Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space . It states: If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and . The theorem and its proof are due to L. E. J. Brouwer, published in 1912. The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem. (Wikipedia).

Invariance of domain
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Subset | Manifold | Inverse function | Local homeomorphism | Domain of a function | Banach space | Lp space | Homeomorphism | L. E. J. Brouwer | Topology | Sequence | Euclidean space | Open set | Algebraic topology