Suppose $F:M\rightarrow N$ is an injective immersion between smooth manifolds. Is there an embedding $F$ such that there is a compact subspace $K$ of $N$ with $F^{-1}(K)$ is not compact?
2026-04-06 14:52:44.1775487164
Example of an embedding $F$ with a given property
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Hint: Take $M, N$ both equal to the open interval $(0, 1)$ and try to find a counter-example.