Journal ArticleDOI
Ein einfacher Beweis des Satzes von Alexandroff-Lester
Reads0
Chats0
TLDR
In this paper, the theorem of ALEXANDROFF-LESTER was extended to non-regular metric vector spaces of characteristic 2, for which counterexamples and a new proof were presented.Abstract:
By presenting counterexamples and a new proof, we determine all metric vector spaces, for which the theorem of ALEXANDROFF-LESTER holds. In this context, the theorem will be extended to certain nonregular metric vector spaces of characteristic 2.read more
Citations
More filters
Book ChapterDOI
Chapter 16 – Distance Preserving Transformations
TL;DR: In this paper, the authors focus on distance preserving transformations of Minkowski space-time, the geometrical space of special relativity theory, where distances need no longer be positive, symmetry disappears and about all that remains is a space with scalars somehow assigned to pairs of its points.
Journal ArticleDOI
On 0-distance-preserving permutations of affine and projective quadrics
TL;DR: In this paper, the question under which conditions an arbitrary permutation ϕ of a quadric satisfying X ≈Y ⇔ Xϕ ≈ Yϕ ∀ X,Y e F can be extended to a collineation of the given space is answered.
Journal ArticleDOI
On 2-closures of rank 3 groups
TL;DR: In this article, it was shown that the 2 -closure of a primitive one-dimensional affine rank 3 group of sufficiently large degree is also affine and 1-dimensional.
Posted Content
Continuous space-time transformations
TL;DR: In this paper, it was shown that every continuous map acting on the four-dimensional Minkowski space and preserving light cones in one direction only is either a Poincar\'e similarity, that is, a product of a Lorentz transformation and a dilation, or it is of a very special degenerate form.
References
More filters
Book
Quadratic and Hermitian Forms
TL;DR: In this article, the authors present a classification of Quadratic Forms over Fields and their application in Fields of Prescribed Level, including the following: 1. Symmetric Bilinear Forms over Dedekind rings and Global Fields.
Journal ArticleDOI
Ensembles quadratiques des espaces projectifs.
TL;DR: In this article, the authors define an ensemble of points as "a family of sous-ensembles appel6s droites, v6rifiant les conditions suivantes (i) toute paire de points distincts p, q est contenue dans une and une seule droite not6e p + q; (ii) tout droite contient au moins trois points; (iii) si a, b, c, d, e sont des points distinct, tels que a + b =
Journal ArticleDOI
The structure of space-time transformations
TL;DR: In this paper, it was shown that a one-to-one mapping of n-dimensional space-time onto itself is an inhomogeneous Lorentz transformation, up to dilatations.
Journal ArticleDOI
Fundamentalsätze der metrischen Geometrie
TL;DR: For arbitrary quadratic forms, including the cases of characteristic 2 and of infinite dimensions, several affine and projective-metric structures are considered, and the corresponding isomorphisms are determined as discussed by the authors.