From: Boudewijn Moonen 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 Nussallee 15 D-53115 Bonn GERMANY e-mail: Boudewijn.Moonen@ipb.uni-bonn.de Tel.: GERMANY +49-228-732910 Fax.: GERMANY +49-228-732712