## Q on Riemann domains

If P is the projection map from a Riemann domain M $\rightarrow C^n$, and U is a connected subset of M with P(U)=B, where B is a ball in $C^n$, then is P injective on U, so it's a homeomorphism on U?
P is locally a homeomorphism by definition.
It would be related to B being simply connected. WOuldn't be true if P(U) were ring-shaped.
I read something saying that in complex analysis, local homeomorphisms being global homeomorphisms relates to connectivity.
If P is proper, meaning if K is a compact subset of B, the inverse image in U of K is compact, it would be true by a theorem of Ho, apparently.
Laura
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