Geodesic
Semiaffine spaces
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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In this paper we improve on a result of Beutelspacher, De Vito & Lo Re, who characterized in 1995 finite semiaffine spaces by means of transversals and a condition on weak parallelism. Basically, we show that one can delete that condition completely. Moreover, we extend the result to the infinite case, showing that every plane of a planar space with at least two planes and such that all planes are semiaffine, comes from a (Desarguesian) projective plane by deleting either a line and all of its points, a line and all but one of its points, a point, or nothing.
DOI : 10.37236/107
Classification : 51A45, 51E15
Mots-clés : semiaffine spaces, transversal 
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     author = {Hendrik Van Maldeghem},
     title = {Semiaffine spaces},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/107},
     zbl = {1169.51005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/107/}
}
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Hendrik Van Maldeghem. Semiaffine spaces. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/107

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