Invariance of domain
![A map which is not a homeomorphism onto its image: g : (−1.1, 1) → R2 with g(t) = (t2 − 1, t3 − t)](/Images/godic/202501/20/A_map_which_is_not_a_homeomorphism_onto_its_image4703.png")
Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space R. It states:
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.