# Something like the weak Whitney embedding theorem for continuous maps and homotopy.

This is sort of a reference request. Consider a continuous map of orientable topological manifolds $f:N\longrightarrow M$ of dimension $n$ and $m$ respectively.

I have been told that there is a theorem something like "if $m>2n$ then $f$ is homotopic to an embedding" however I am having trouble finding such a result. We have this in the form of Whitney's embedding theorem if the manifolds are smooth but I am wondering about the more general case of a topological manifold (most importantly I want to relax the conditions to just a continuous map, not a smooth one).

Maybe there are some further hypotheses needed like $M$ being closed or compact, or simply connected. Can anyone point me to a reference for such a theorem?

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Maybe this is contained in the weak embedding theorem. I don't have a good reference for any of this stuff beyond wiki. –  AnonymousCoward May 7 '12 at 2:33
I believe this answers my question mathoverflow.net/questions/34658/… –  AnonymousCoward May 7 '12 at 2:34