Semiaffine stable planes

A locally compact stable plane of positive topological dimension will be called semiaffine if for every line L and every point p not in L there is at most one line passing through p and disjoint from L . We show that then the plane is either an affine or projective plane or a punctured projective pl...

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Bibliographic Details
Published in:Beiträge zur Algebra und Geometrie 2023-11
Main Authors: Löwen, Rainer, Stroppel, Markus J.
Format: Article
Language:English
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Summary:A locally compact stable plane of positive topological dimension will be called semiaffine if for every line L and every point p not in L there is at most one line passing through p and disjoint from L . We show that then the plane is either an affine or projective plane or a punctured projective plane (i.e., a projective plane with one point deleted). We also compare this with the situation in general linear spaces (without topology), where P. Dembowski showed that the analogue of our main result is true for finite spaces but fails in general.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-023-00720-z