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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 Dan Rust, Seirios, Andrey Rekalo, Start wearing purple, Zev Chonoles Jul 7 '13 at 15:03

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up vote 4 down vote accepted

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

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