My question might be broad. Let $E$ be the covering space of $B$, what do we know about the embedding of $E$ (into some space)? I am looking for some general results or references.
EDIT: After Lee Mosher's comment:
I could make it bit specific, for example, if the space $B$ admits triangulation or is a compact n-manifold. What can we say about the embedding of $E$. I found the following result here
If $f:X\rightarrow Y$ is an $r$-sheeted covering space with $X$ being a compact topological space, then $Y$ embedds in Euclidean space $\mathbb{R}^{2k+1}$ for some natural $k$.
The proof follows from Whitney embedding theorem since by above link, $Y$ is compact.
Though I wanted some general results, my specific problem is for the space $B$ admitting triangulation.