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Dec 18, 2022 at 14:07 comment added dennis @PiotrHajlasz Thanks but is this still true in the 'vicinity' of Euclidean space (as proposed in my question)?
Oct 2, 2022 at 0:24 history edited LSpice CC BY-SA 4.0
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Oct 1, 2022 at 21:15 history edited Piotr Hajlasz CC BY-SA 4.0
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Oct 1, 2022 at 21:10 comment added Piotr Hajlasz @AndyPutman You are absolutely right. I wrote my answer without thinking enough.
Oct 1, 2022 at 20:54 comment added Andy Putman Aren't you also assuming that the normal bundle of $\Sigma$ is trivial? Otherwise, the tubular neighborhood won't split as a product.
Oct 1, 2022 at 20:50 history answered Piotr Hajlasz CC BY-SA 4.0