Semiaffine stable planes

IF 0.4 Q4 MATHEMATICS
Rainer Löwen, Markus J. Stroppel
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引用次数: 0

Abstract

Abstract 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.
半机械人计划
如果在L以外的每条直线L和每一个点p至少有一条直线经过p且与L不相交,则称为半仿射的局部紧稳定平面。我们证明了这个平面要么是仿射平面,要么是射影平面,要么是刺破的射影平面(即去掉一个点的射影平面)。我们还将其与一般线性空间(没有拓扑)的情况进行了比较,其中P. Dembowski表明,我们的主要结果的模拟对于有限空间是正确的,但在一般情况下是失败的。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
56
期刊介绍: The Journal "Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry" was founded in 1971 on the occasion of the 65th birthday of O.-H. Keller. It publishes research articles in the areas of algebra, geometry, algebraic geometry and related fields, preferably in English language. The back issues of the journal are available at the European Digital Mathematics Library (EuDML) at: https://eudml.org/journal/10170 (Vols. 1-33, 1971-1992) https://eudml.org/journal/10084 (Vols. 34-51, 1993-2010)
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