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GENERALIZATIONS OF THE FUNDAMENTAL THEOREM OF PROJECTIVE GEOMETRY.
- Source :
-
Bulletin of the Australian Mathematical Society . Oct2009, Vol. 80 Issue 2, p350-352. 3p. - Publication Year :
- 2009
-
Abstract
- The article presents a thesis discussing the fundamental theorem of projective geometry, which states that a semilinear transformation induces every line-preserving bijection of a Desaguersian projective plane. It is stated that the theorem extends to higher-dimensional projective spaces, affine transformations and even to buildings, which are combinatorial constructions. It considers the spaces' bijections preserving their geometry such as the transformations of quasi-spheres and proves local versions of theorems on arbitrary nondiscrete fields. Details on the parts of the thesis, which include a review of the theorem, nondiscrete topological fields and hypotheses involving measurable sets, are presented.
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 80
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 45386235
- Full Text :
- https://doi.org/10.1017/S0004972709000689