Let $M$ and $N$ be two smooth manifolds and $f:M\to N$ be an injective immersion. Let $U\subset M$ be an open subset, then is $f(U)$ necessarily a Borel measurable subset of $N$?
2026-04-06 10:56:50.1775473010
Image of an open set under an injective immersion map is Borel measurable?
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You can just cover U with open subsets where f is an imbedding. Then f(U) is a countable union of borel measurable sets
Edit: Daniel’s answer in the comments is obviously better