Index
$S^2\setminus\text{point}$
$S^2\setminus S^0$
$S^2\setminus S^1$

This illustrates the fact that $S^2\setminus\text{point}$ is contractible. In more detail: the full sphere is $S^2$, and we remove the north pole, which is marked in green. The resulting space can be peeled back to the south pole (marked in red), so it is contractible. Alternatively, we have seen that $S^2\setminus\text{point}$ is homeomorphic to $\mathbb{R}^2$ by stereographic projection, and $\mathbb{R}^2$ is contractible by a linear homotopy, so $S^2\setminus\text{point}$ is also contractible.