1. PF Insights is off to a great start! Fresh and interesting articles on all things science and math. Here: PF Insights

Q on Riemann domains

  1. 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 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
     
    Last edited: Feb 3, 2009
  2. jcsd
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?

0
Draft saved Draft deleted
Similar discussions for: Q on Riemann domains
Loading...