A Helly property of arcs
type: Item
instance of: scholarly article
title: A Helly property of arcs
zbMATH Open document ID: 0655.52002
DOI: 10.1007/BF01194393
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: If \(n+1\) arcs are given in the n-cube, each joining (0,...,0) to (1,...,1), then there is an arc joining the same points, and which is in between each n of the given arcs. The result is false for less than \(n+1\) arcs. The involved concept of betweenness is a natural one and relates with a convexity on the space of all arcs. The above result (which will be derived for n-dimensional compact arcwise connected Heyting algebras) can be compared with the classical Helly Theorem for Euclidean space.
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 54H12
zbMATH DE Number: 4069702
zbMATH Keywords: convex set
zbMATH Keywords: generalized cube
zbMATH Keywords: Helly number
zbMATH Keywords: Heyting algebra
zbMATH Keywords: Lawson semilattice
zbMATH Keywords: arcs
author: Marcel van de Vel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4069702