Grassmann spaces of regular subspaces
type: Item
instance of: scholarly article
title: Grassmann spaces of regular subspaces
zbMATH Open document ID: 1204.51019
published in: Journal of Geometry
publication date: 2010-10-29T00:00:00Z
review text: Let \(\mathfrak{A}\) be a metric affine space and \(\mathfrak{P}\) be a metric projective space over a field \(F\) with \(\text{char}F\neq2\), where the metric is given by a bilinear form. A certain substructure of \(\mathfrak{A}\), respectively \(\mathfrak{P}\), is called a Grassmann space. The authors recover the original geometry from its Grassmann space. The investigations of the paper are parts of two (or even three) meta-geometrical problems: to characterize sufficient notions for a (geometrical) theory, to interpret one theory in another one, and to show axiomatizability of some class of structures.
Mathematics Subject Classification ID: 51F99
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 5808435
zbMATH Keywords: metric affine geometry
zbMATH Keywords: metric projective geometry
zbMATH Keywords: orthogonality
zbMATH Keywords: regular subspace
zbMATH Keywords: Grassmann space
zbMATH Keywords: axiomatizability
author: M. Prażmowska
author: K. Prażmowski
author: M. Żynel
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: s00022-010-0040-4
OpenAlex ID: W1992159686
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DOI: 10.1007/S00022-010-0040-4
description: scientific article; zbMATH DE number 5808435