Let $p$ and $q$ be two points of $\mathbb{R}^n$ where let $n\geq 1$. Then
$\dim H^k(\mathbb R^n - p - q) = \begin{cases}0, &\text{ if }k\text{ is not equal to }n-1,\\ 2,&\text{ if }k = n-1.\end{cases}$
I'm trying to prove this, but I've thought of letting $S = \{p,q\}$ and using the fact that the open set of $\mathbb R^{n+1} - S\times \mathbb{R}^1$ of $\mathbb R^{n+1}$ is homologically trivial in all dimensions.