A Krasnosel'skii theorem for open finitely starlike sets in \(R^ 3\)
type: Item
instance of: scholarly article
title: A Krasnosel'skii theorem for open finitely starlike sets in \(R^ 3\)
zbMATH Open document ID: 0718.52008
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: A set S in Euclidean d-space \({\mathbb{R}}^ d\) is called finitely starlike if every finite subset of S sees via S a common point. The main result of this paper says that an open set \(S\subset {\mathbb{R}}^ 3\) is finitely starlike if every seven points in S see via S a common point, and if for every three points x,y,z\(\in S\) which see each other via S the inclusion cov\(\{\) x,y,z\(\}\subseteq S\) holds true.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 4184292
zbMATH Keywords: starshaped set
zbMATH Keywords: finitely starlike set
author: Marilyn Breen
MaRDI profile type: Publication
description: scientific article