Feb3-09, 04:56 AM
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.
|Register to reply|
|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|