Spaces with congruence

Alexander Kreuzer; Kay Sörensen

doi:10.1016/j.disc.2006.11.034

Spaces with congruence

Alexander Kreuzer
, Kay Sörensen

Department of Mathematics

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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AU - Sörensen, Kay

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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.

KW - Congruence

KW - Line reflections

KW - Motions

UR - https://www.scopus.com/pages/publications/36248980459

U2 - 10.1016/j.disc.2006.11.034

DO - 10.1016/j.disc.2006.11.034

M3 - Article

AN - SCOPUS:36248980459

SN - 0012-365X

VL - 308

SP - 207

EP - 213

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2-3

ER -

Spaces with congruence

Abstract

Keywords

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