Incidence manifolds
type: Item
instance of: scholarly article
title: Incidence manifolds
zbMATH Open document ID: 0713.51003
DOI: 10.1007/BF01230372
published in: Journal of Geometry
publication date: 1990-01-01T00:00:00Z
review text: The h-th Grassmann space associated with a projective space P is the incidence structure induced on the set of h-flats in P by the residues of all (h-1)-flats and all \((h+1)\)-flats in P by the residues of all (h-1)- flats and all \((h+1)\)-flats and their intersections. Segre's product space associated with two projective spaces consists of the cartesian product \(P_ 0\times P_ 0'\) of the point sets together with all sets of the form \(\{\) \(p\}\times X\) and \(X\times \{p\}\) where p is a point and X is a line or the entire point set of one factor. The paper under review survey and complements various axiomatic characterizations of these objects, both as incidence structures and as topological incidence structures (the latter corresponding to topological projective spaces).
Mathematics Subject Classification ID: 51H25
Mathematics Subject Classification ID: 51H10
zbMATH DE Number: 4173784
zbMATH Keywords: Grassmann's product manifold
zbMATH Keywords: Segre's product space
zbMATH Keywords: incidence structures
zbMATH Keywords: topological incidence structures
author: Corrado Zanella
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01230372
OpenAlex ID: W4246648447
description: scientific article; zbMATH DE number 4173784