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Embbeding topological manifold in euclidean space
Posted:
Jul 9, 2011 8:47 AM
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From: Rodolfo Conde <rcm@gmx.co.uk>
Date: July 8, 2011 7:31:46 PM MDT
To: <sci-math-research@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?
]
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