From: Boudewijn Moonen <Boudewijn.Moonen@ipb.uni-bonn.de>
Subject: Re: local diffeo & RP^n
Date: Fri, 11 Aug 2000 15:45:40 +0200
Newsgroups: sci.math
Summary: [missing]

cwwongreborn wrote:
> 
> have i missed something?
> 
> according to lena's original post, the mapping is only a local
> diffeomorphism between the real projective space RP^n. must it be a
> surjection?
> 
> should it be included in the hypothese of the assertion? or is it a
> consequence of the assumption of being a "loc diff"?
> 
> if not, what will be a counterexample?
> 

Let f : M --> N be a local diffeomorphism of closed ( = compact
borderless) connected manifolds. Then f(M) is both open and closed 
in N, whence f is surjective.


Regards,



-- 
    Boudewijn Moonen
    Institut fuer Photogrammetrie der Universitaet Bonn
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