Is a subset of $\mathbb{R}^{n}$ that is homeomorphic to $\mathbb{R}^{n}$ necessarily open? [duplicate]

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Let $A$ be a subset of $\mathbb{R}^{n}$, such that $A$ is homeomorphic to $\mathbb{R}^{n}$.

Is $A$ open in $\mathbb{R}^{n}$?

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marked as duplicate by Daniel Rust, Seirios, Andrey Rekalo, O.L., Zev ChonolesJul 7 at 15:03

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1 Answer

Yes. This is a special case of the theorem of invariance of domain.

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