On a relation between the nonconvexity of a set and the nonconvexity of its \(\epsilon\)-neighborhood
type: Item
instance of: scholarly article
title: On a relation between the nonconvexity of a set and the nonconvexity of its \(\epsilon\)-neighborhood
zbMATH Open document ID: 1029.46013
DOI: 10.1023/A:1010258909731
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: The authors present examples of sets whose nonconvexity functions substantially differ from the nonconvexity functions of arbitrarily small neighborhoods of these sets. Moreover, it is shown that, in uniformly convex Banach spaces, conditions of the type ``the function of nonconvexity is less than one'' are stable with respect to taking \(\varepsilon\)-neighborhoods of sets.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 52A99
zbMATH DE Number: 1927762
zbMATH Keywords: nonconvexity
author: Dušan Repovš
author: Pavel V. Semenov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1010258909731
OpenAlex ID: W14929577
description: scientific article; zbMATH DE number 1927762