I am doing a problem where I am stuck at this point.
Let $M$ be a connected smooth manifold of dimension $n$ and let $X$ be any subset of $M$. Assume that there is a positive integer $m$ such that $n>2m, ~\dim X < n-m$ and $\pi_m(M-X)=0$. Then is it true that $\pi_m(M)=0$?
Here $\dim X$ is the topological dimension of the space $X$. If $X$ is a submanifold, I guess this result is true.
Any hint/reference will be appreciated.