Helly-type theorems for intersections of sets starshaped via orthogonally convex paths
type: Item
instance of: scholarly article
title: Helly-type theorems for intersections of sets starshaped via orthogonally convex paths
zbMATH Open document ID: 1276.52009
published in: Aequationes Mathematicae
publication date: 2012-12-19T00:00:00Z
review text: The author obtains Helly-type theorems in the framework provided by the replacement of the straight-line segment by the path that is orthogonally convex. The main result refers to a given family \(\mathcal{K}\) of simply connected sets in the plane. It states that if every subfamily of \(\mathcal{K}\) has a starshaped via orthogonally convex path intersection then the family \(\mathcal{K}\) itself has such an intersection. The particular \(d\)-dimensional and finite cases are discussed.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 6116952
zbMATH Keywords: sets starshaped via convex paths
zbMATH Keywords: Helly-type theorems
author: Marilyn Breen
MaRDI profile type: Publication
full work available at URL: s00010-012-0151-0
OpenAlex ID: W1984079904
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DOI: 10.1007/S00010-012-0151-0
description: scientific article; zbMATH DE number 6116952