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#### ModusPonens

##### Well-known member

- Jun 26, 2012

- 45

Is it true that, in $\mathbb{R}^2$ the compact, connected 2-manifolds are determined by the number of holes in them? I think I saw this result somewhere, but I don't remember for sure.

If this is true would that mean that any compact connected set with non empty interior in $\mathbf{C}$ is homeomorphic to the closed unit ball (or disk)?

Thank you in advance.