Sets which are almost starshaped
type: Item
instance of: scholarly article
title: Sets which are almost starshaped
zbMATH Open document ID: 0926.52008
DOI: 10.1007/BF01237598
author: J. Cel
published in: Journal of Geometry
publication date: 1998-10-27T00:00:00Z
review text: According to [\textit{J. Cel}, J. Geom. 53, No. 1-2, 28-36 (1995; Zbl 0831.52003)], a closed connected nonconvex set \(S\) in \(R^d\) with a bounded subset of local nonconvexity points is starshaped if and only if every \(d+1\) or fewer such points are clearly visible via \(S\) from a common point. An analogous criterion for \(S\) open, connected and nonconvex was established by the author in [Geom. Dedicata 66, No. 3, 293-301 (1997; Zbl 0908.46005)]. In the present paper, the author obtains a characterization of a similar type for sets which are neither closed nor open. This generalizes a planar result by \textit{M. Breen} [Geom. Dedicata 13, 201-213 (1982; Zbl 0511.52004)].
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 1200020
zbMATH Keywords: starshaped set
zbMATH Keywords: Krasnosel'skii-type theorem
zbMATH Keywords: local nonconvexity points
reviewed by: B. V. Dekster
MaRDI profile type: Publication
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cites work: Unsolved problems in geometry
cites work: Q5338702
full work available at URL: https://doi.org/10.1007/bf01237598
OpenAlex ID: W10323519
description: scientific article; zbMATH DE number 1200020