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Question: Is every compact contractible subset of $\mathbb{R}^n$ homeomorphic to a closed ball of some dimension?

This post doesn't quite answer my question because it is about open sets.

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    – Alessandro Codenotti
    Commented Jun 9, 2022 at 1:02

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No!! For example consider Mazur manifold (https://en.wikipedia.org/wiki/Mazur_manifold) which can be embedded in $\mathbb R^4$ [to see this, take double of it, which is $S^4$, and remove a point]. But it is not homeomorphic to any ball as it's boundary is not a sphere.

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