Register to reply 
Q on Riemann domains 
Share this thread: 
#1
Feb309, 04:56 AM

P: 164

If P is the projection map from a Riemann domain M [itex]\rightarrow C^n[/itex], and U is a connected subset of M with P(U)=B, where B is a ball in [itex]C^n[/itex], 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 ringshaped. 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 


Register to reply 
Related Discussions  
What bracket is used to denote a number is excluded from a domain?  General Math  2  
Trying to determine domain of f(t)=4.5e^t  General Math  7  
Finding the maximum domains  General Math  6  
Magnetic domains...what are they?  General Physics  1  
Who owns domains?  Computing & Technology  9 