Limits of starshaped sets
type: Item
instance of: scholarly article
title: Limits of starshaped sets
zbMATH Open document ID: 0603.46014
DOI: 10.1007/BF01195358
author: Victor Klee
author: Gerald Beer
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: This paper discusses relationships among collections of limits of sequences of bounded closed starshaped subsets of a normed linear space E. Three different modes of convergence are considered, one being convergence with respect to the Hausdorff metric. The main results show that the completeness of E, the reflexivity of E, and the finite- dimensionality of E can all be characterized in terms of equality between certain collections of limits of starshaped sets. Also included are necessary and sufficient conditions for the Hausdorff metric limit of a given sequence of sets to be starshaped from a given point.
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 3973576
zbMATH Keywords: Kuratowski convergence
zbMATH Keywords: convergence with respect to the Hausdorff metric
zbMATH Keywords: completeness
zbMATH Keywords: reflexivity
zbMATH Keywords: equality between certain collections of limits of starshaped sets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3973576