# Is there any manifold that is not a subspace of a finite dimensional euclidean space?

I mean, is there any topological space that is locally euclidean, Haudorff and second countable and can't be embedded into a finite dimensional Euclidean space. I think it's hard for me to find such spaces because manifolds are often described visually as an euclidean subspace..

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No, there is no. This is the 'embedding thm' for manifolds. – Berci Jan 23 '13 at 14:32
I'm not sure, but someone says that it's a special case, when the space is 'riemannian'.. – Lee Dae Seok Jan 23 '13 at 15:05

A separable metric space that has dimension $n$ (in the sense of topological dimension) may be embedded in Euclidean space of dimension at most $2n+1$.