On exercise 6 of chapter 11 of "Comprehensive Introduction to Differential Geometry" by Spivak, one is asked to apply the exact sequence for the pair $(S^n \times R^m,\{p\}\times R^m)$ to calculate $H_c^k(S^n \times R^m)$. This is simple, but one thing is bothering me: the hypothesis of the theorem that assures the existence of such exact sequence for the pair $(M,N)$ requires that $N$ be a compact submanifold of $M$, and I can't see why $\{p\}\times R^m$ is a compact submanifold of $S^n \times R^m$.
The answer can be a bit stupid, but I've tried some ideas and got stuck. Any hints would be great.