Infinite dimensions for ordered incidence geometry
type: Item
instance of: scholarly article
title: Infinite dimensions for ordered incidence geometry
zbMATH Open document ID: 0686.51006
DOI: 10.1007/BF01231030
published in: Journal of Geometry
publication date: 1989-01-01T00:00:00Z
review text: In J. Geom. 30, 103-122 (1988; Zbl 0629.51013), \textit{A. Ben-Tal} and \textit{A. Ben-Israel} have set up an abstract conexity theory based on the notions of incidence, order, affine hull and dimension. Although they incorporate the case of infinite dimensions into their axiomatic setting, their work mainly refers to finite dimensional geometries and seems to need some refinements as for the infinite dimensional case. This is done in the paper under review. By a few minor modifications to the axioms and to the results, the author establishes Ben-Tal's and Ben-Israel's theory for arbitrary dimensions. In particular, he gives a version of the hyperplane separation theorem for infinite dimensional ordered incidence geometries.
Mathematics Subject Classification ID: 51G05
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 4124473
zbMATH Keywords: ordered spaces
zbMATH Keywords: Radon and Helly type theorems
zbMATH Keywords: abstract conexity
zbMATH Keywords: hyperplane separation theorem
author: John B. Strantzen
reviewed by: Franz B. Kalhoff
MaRDI profile type: Publication
cites work: Ordered incidence geometry and the geometric foundations of convexity theory
cites work: Q5635941
cites work: Q3854260
full work available at URL: https://doi.org/10.1007/bf01231030
OpenAlex ID: W2064705164
description: scientific article; zbMATH DE number 4124473