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Possible Duplicate:
Is there a Whitney Embedding Theorem for non-smooth manifolds?

A topological space $X$ is locally Euclidean if for each $p\in X$ there is neighbourhood which is homeomorphic to an open subset of $\mathbb{R}$.

What are the locally euclidean topological spaces which can be embeded in $\mathbb{R}^n$?

I know they have to be Hausdorff obviously because the line with two origins is a locally euclidean but is not Hausdorff. What are the minimal topological properties wich our topological space doesn't have that are nessesary to be embeded in $\mathbb{R}^n$?

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2 
 mathoverflow.net/questions/34658/… – Qiaochu Yuan Aug 11 2011 at 18:31
@Qiaochu :Thank you, that question is similar to mine; but not the same. – dan232 Aug 11 2011 at 19:23
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 This is not really a duplicate, since "topological manifold" has different meanings in the two questions. I'm voting to reopen. See meta.mathoverflow.net/discussion/1111/… – Kevin Walker Aug 11 2011 at 20:11
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 @kevin: In the books I read, a topological manifold is a topological space such that exists an $n\in\mathbb{N}$ so that $X$ is locally Euclidean. You can check wikipedia, in the english article it sais that it's hausdorff but if read the spanish one, it sais that hausdorffness is not nessesary. I guess this terminology variates from one country to another. en.wikipedia.org/wiki/Topological_manifold – dan232 Aug 11 2011 at 20:29
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 I didn't say it was wrong. I said that's what I understand for "topological manifold", but I'll changed it if you like. – dan232 Aug 11 2011 at 21:01
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closed as exact duplicate by Qiaochu Yuan, José Figueroa-O'Farrill, André Henriques, Dmitri Pavlov, Theo Johnson-Freyd Aug 11 2011 at 20:00

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