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overheard a joke about some topological space where one can go in but can't come out. What is the name of this space. Google just gave me black holes.

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Could that be a Klein bottle? One can go in, but once in, one can't come out, since the inside and the outside of a Klein bottle are the same.

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    @MaoYiyi Certainly, but the check mark ✓, not the up-arrow ⇮, is used for accepting. If I were you, I would undo the check mark, and wait a day or two to see if any better answers come in, before accepting.2012-09-14