Mirror property for nonsingular mixed configurations of lines and points in \(\mathbb{R}^ 3\)
type: Item
instance of: scholarly article
title: Mirror property for nonsingular mixed configurations of lines and points in \(\mathbb{R}^ 3\)
zbMATH Open document ID: 0805.51003
DOI: 10.1007/BF02574011
published in: Discrete \& Computational Geometry
publication date: 1995-01-31T00:00:00Z
full work available at URL: https://eudml.org/doc/131304
review text: Let \(M(h,k)\) denote the topological space whose points are the sets of \(h\) lines and \(k\) points of \(\mathbb{R}^ 3\) in general position. An element of \(M(h,k)\) is said to be mirror if there exists a continuous path in \(\mathbb{R}^ 3\) joining it with its image after reflection in a plane of \(\mathbb{R}^ 3\), and nonmirror otherwise. The question considered here is which \(M(h,k)\) contains mirror elements and which ones contain nonmirror elements. The problem is solved for all cases except when \(h\equiv 1\pmod 4\) with \(h\geq 5\) and \(k=2\) or 3.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51H99
zbMATH DE Number: 590855
zbMATH Keywords: points and lines in general position
zbMATH Keywords: mirror property
author: Alberto Borobia
reviewed by: Ferdinand D. Veldkamp
MaRDI profile type: Publication
cites work: Q4037345
cites work: Q4204259
cites work: Q3711242
cites work: Q5753121
description: scientific article; zbMATH DE number 590855