Invariance of domain
Theorem in topology about homeomorphic subsets of Euclidean space / From Wikipedia, the free encyclopedia
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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.[1] The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem.