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Embbeding topological manifold in euclidean space
Posted:
Jul 9, 2011 8:47 AM


From: Rodolfo Conde <rcm@gmx.co.uk> Date: July 8, 2011 7:31:46 PM MDT To: <scimathresearch@moderators.isc.org> Subject: Embbeding topological manifold in euclidean space
Hi all,
Is there an easy proof of the fact that every topological manifold (no additional structure) embbeds in an euclidean space R^q, no matter how big q is ??
Thanks in advance...
cheers...
[ Moderator's Note.
Indeed, a separable metric space with topological dimension n embeds in R^{2n+1}, a result of Menger, N\"obeling, Lefschetz. So I guess the question is: Is there a simpler proof if we relax the dimension 2n+1 into which we embed, and/or if we are only interested in manifolds? ]



