The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.
| Identifer | oai:union.ndltd.org:ADTP/258065 |
| Date | January 2009 |
| Creators | McCallum, Rupert Gordon, Mathematics & Statistics, Faculty of Science, UNSW |
| Publisher | Publisher:University of New South Wales. Mathematics & Statistics |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://unsworks.unsw.edu.au/copyright, http://unsworks.unsw.edu.au/copyright |
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