# What locally euclidean topological spaces are embeded in $\mathbb{R}^n$? [duplicate]

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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@Qiaochu :Thank you, that question is similar to mine; but not the same. –  dan232 Aug 11 '11 at 19:23
This is not really a duplicate, since "topological manifold" has different meanings in the two questions. I'm voting to reopen. See tea.mathoverflow.net/discussion/1111/… –  Kevin Walker Aug 11 '11 at 20:11
@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 '11 at 20:29
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 '11 at 21:01