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What is example of a simply connected Lipschitz domain which is not homeomorphic to unit ball? In $R^2$, such a domain is necessarily unit disc (Are simply connected open sets in $\mathbb{R}^2$ homeomorphic to an open ball?).

Even, I am curious to just see the example without being "Lipschitz".

ersh
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    Maybe $\mathbb{R}^3 \backslash {0}$? – Aphelli Jan 06 '19 at 20:11
  • Right, that is the example of a simply connected domain! But this doesn't have a Lipschitz boundary? Now, if I consider a three dimensional open-annulus which is simply connected having boundry as the union of two spheres, I think this would constitute the Lipschitz domain? – ersh Jan 06 '19 at 20:29
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    I think so, indeed, since the boundary is going to be a smooth $2$-dimensional manifold. – Aphelli Jan 06 '19 at 20:32

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