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?