Topological affine spaces
type: Item
instance of: scholarly article
title: Topological affine spaces
zbMATH Open document ID: 0686.51007
DOI: 10.1007/BF01222275
author: Corrado Zanella
published in: Journal of Geometry
publication date: 1989-01-01T00:00:00Z
review text: \textit{K. Sörensen} [Beitr. Geom. Algebra, Proc Symp. Duisburg 1976, 305- 310 (1977; Zbl 0381.51008)] defined a topological affine space using topologies for the set of points and for the set of hyperplanes such that the joining of n independent points, the intersection of n independent hyperplanes and the constructions of parallel hyperplanes are continuous operations. Now a characterization of such spaces is given by means of the topologies on the sets of points and lines using the continuity of the following geometric operations (when defined): A1) joining of two points, A2) interseting two lines, A3) drawing the parallel line, A4) intersecting lines with a given hyperplane. For dimension two both notions coincide.
Mathematics Subject Classification ID: 51H10
zbMATH DE Number: 4124474
zbMATH Keywords: topological affine space
MaRDI profile type: Publication
cites work: Sur les espaces projectifs topologiques
cites work: Topologische projektive Räume
description: scientific article; zbMATH DE number 4124474