Finitely starlike sets whose F-stars have positive measure
type: Item
instance of: scholarly article
title: Finitely starlike sets whose F-stars have positive measure
zbMATH Open document ID: 0691.52005
DOI: 10.1007/BF01222258
author: Marilyn Breen
published in: Journal of Geometry
publication date: 1989-01-01T00:00:00Z
review text: Krasnoselskij's classical theorem characterizes compact starshaped sets in Euclidean spaces. Without the assumption of compactness the corresponding results become much more intricate. The present article describes, among other things, such a situation in the Euclidean plane, with much zeal and ingenuity. Given a planar set S, we say that X sees Y via S, if every line connecting some point of X to some point of Y belongs to S. Let T be the interior of the closure of S. If \(T\setminus S\) is small, in a sense to be made precise, then every finite subset X of S sees some subset L(X) with positive area, via S, provided that every fourpointed subset of S does.
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 4131166
zbMATH Keywords: starlike set
zbMATH Keywords: visible
zbMATH Keywords: Lebesgue measure
reviewed by: P. Mani-Levitska
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4131166