Invariance Of Domain


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What is Invariance of domain?

Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space ℝn. It states: If U is an open subset of ℝn and f : U → ℝn is an injective continuous map, then V := f(U) is open in ℝn and f is a homeomorphism between U and V. 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.

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algebraic topologyhomeomorphismmathematical theorempropositionstatementtheoremtheorems in topologytheory


Brouwer's theorem on domain invarianceDomain invariance theorem


Invarianza del dominio (es)Théorème de l'invariance du domaine (fr)Twierdzenie Brouwera o zachowaniu otwartości (pl)Теорема об инвариантности области (ru)

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 — Date merged: 11/6/2021, 1:32:46 PM
 — Date scraped: 5/20/2021, 6:19:22 PM