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{\bf Hendrik Van Maldeghem}
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{\bf Semiaffine Spaces}
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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.



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