Abstract
We deal with a natural generalization of the classical Fundamental Theorem of Affine Geometry to the case of non bijective maps. This extension geometrically characterizes semiaffine morphisms. It was obtained by W. Zick in 1981, although it is almost unknown. Our aim is to present and discuss a simplified proof of this result.
Publisher
Universidad de Extremadura - Servicio de Publicaciones
Subject
Geometry and Topology,Mathematics (miscellaneous),Algebra and Number Theory,Analysis
Reference19 articles.
1. S. Artstein-Avidan, B.A. Slomka, The fundamental theorems of affine and projective geometry revisited, Commun. Contemp. Math. 19 (5) (2017), 1650059, 39 pp.
2. M.K. Bennett, “ Affine and projective geometry ”, John Wiley & Sons, Inc., New York, 1995.
3. M. Berger, “ Geometry I ”, Springer-Verlag, Berlin, 1987.
4. A. Beutelspacher, U. Rosenbaum, “ Projective geometry: from foundations to applications ”, Cambridge University Press, Cambridge, 1998.
5. A. Chubarev, I. Pinelis, Fundamental theorem of geometry without the 1-to-1 assumption, Proc. Amer. Math. Soc. 127 (9) (1999), 2735 – 2744.