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Let $X$ be a non-compact manifold without boundary. Suppose that $b_1(X)=0$. Suppose $Y$ is a codimension zero compact submanifold with corner.

Q Can we find a compact submanifold $Z$ with smooth boundary such that $Y\subset Z\subset X$ and $b_1(Z)=0$.

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  • $\begingroup$ Can you tell us please what or where the boundary of $Z$ should be? $\endgroup$ – Sebastian Goette Sep 13 at 23:26

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