Spaces with congruence

Alexander Kreuzer; Kay Sörensen

doi:10.1016/j.disc.2006.11.034

Spaces with congruence

Alexander Kreuzer, Kay Sörensen

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Technical University of Munich

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider an exchange space with congruence (P, L, ≡) not assuming any further geometrical properties. If the dimension of the space is greater than 2, we show that for any line G of a plane E and any point x ∈ G there is a unique perpendicular line through x in E and that any line reflection is a motion.

Original language	English
Pages (from-to)	207-213
Number of pages	7
Journal	Discrete Mathematics
Volume	308
Issue number	2-3
DOIs	https://doi.org/10.1016/j.disc.2006.11.034
State	Published - 6 Feb 2008

Keywords

Congruence
Line reflections
Motions

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10.1016/j.disc.2006.11.034

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title = "Spaces with congruence",

abstract = "In this paper we consider an exchange space with congruence (P, L, ≡) not assuming any further geometrical properties. If the dimension of the space is greater than 2, we show that for any line G of a plane E and any point x ∈ G there is a unique perpendicular line through x in E and that any line reflection is a motion.",

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AB - In this paper we consider an exchange space with congruence (P, L, ≡) not assuming any further geometrical properties. If the dimension of the space is greater than 2, we show that for any line G of a plane E and any point x ∈ G there is a unique perpendicular line through x in E and that any line reflection is a motion.

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KW - Motions

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DO - 10.1016/j.disc.2006.11.034

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JO - Discrete Mathematics

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Spaces with congruence

Abstract

Keywords

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