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A remark on polar geometry

A remark on polar geometry Abh. Math. Sem. Univ. Hamburg 61 (1991), 213-215 By A. KREUZER Dedicated to Professor Dr. WALTER BENZ on the occasion of his sixtieth birthday It will be shown that the definition of polar geometry in [2], [3] by E VELDKAMP is equivalent to the definition by J. Tlxs [1]. In [2], [3] E VELDKAMP introduced the notion of polar geometry as a partially ordered set (S, _<), satifying the following axioms (For more details see [2] p.527; [3] p.194): IIl. If T is a non empty subset of S, then inf T the infimum of T exists. Let 0 := inf S and for x,y E S let x/X y := inf{x, y} and x v y := sup{x,y}, if the supremum sup{x,y} of {x,y} exists. By M we denote the set of all maximal elements. IV. If z ~ S, then z__ := {x 6 S : x < z} is a projective space of finite rank, called the rank of z. V. Every element of S is contained in a maximal element. All maximal elements have the same finite rank i(S) > 3. VI. If p A q = O, then there are o,b E M such http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

A remark on polar geometry

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References (4)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/BF02950766
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Abstract

Abh. Math. Sem. Univ. Hamburg 61 (1991), 213-215 By A. KREUZER Dedicated to Professor Dr. WALTER BENZ on the occasion of his sixtieth birthday It will be shown that the definition of polar geometry in [2], [3] by E VELDKAMP is equivalent to the definition by J. Tlxs [1]. In [2], [3] E VELDKAMP introduced the notion of polar geometry as a partially ordered set (S, _<), satifying the following axioms (For more details see [2] p.527; [3] p.194): IIl. If T is a non empty subset of S, then inf T the infimum of T exists. Let 0 := inf S and for x,y E S let x/X y := inf{x, y} and x v y := sup{x,y}, if the supremum sup{x,y} of {x,y} exists. By M we denote the set of all maximal elements. IV. If z ~ S, then z__ := {x 6 S : x < z} is a projective space of finite rank, called the rank of z. V. Every element of S is contained in a maximal element. All maximal elements have the same finite rank i(S) > 3. VI. If p A q = O, then there are o,b E M such

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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Sep 8, 2008

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