What are some surprising facts that happen after you remove a point to a space? [closed]

There are some facts that are really impressive after you remove a point to a space. Some typical examples are the existence of exotic spheres or the fact that $S^4$ is not almost complex. Or some not differentiable manifolds that become differentiable manifold after removing a point.

closed as unclear what you're asking by YCor, Ian Morris, abx, Pace Nielsen, Alexandre EremenkoJun 19 '18 at 20:44

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