Denting points of convex sets and weak property \((\pi)\) of cones in locally convex spaces
type: Item
instance of: scholarly article
title: Denting points of convex sets and weak property \((\pi)\) of cones in locally convex spaces
zbMATH Open document ID: 1471.46006
author: Yanyan Li
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2021-06-15T00:00:00Z
review text: The authors continue their work on the geometry of sets in a locally convex space \((E, \tau)\). Analogous to the well-studied case of normed linear spaces, the authors first introduce stronger notions of extremality for a convex set \(C\subset E\), like strongly extreme and denting points of a set. It is shown that a denting point is a strongly extreme point. When some of these notions are considered w.r.t. the weak topology \(\sigma(E,E^\ast)\), a strong extreme point \(x \in C\) (assuming that for a neighbourhood \(U\) of \(x\), \(C\cap U\) is a bounded convex set), is then characterized in terms of a family of open slices of \(C \cap U\) containing \(x\), forming a local base for \(x\) in the relative topology on \(C \cap U\). One misses the mention of the work of H. P. Rosenthal in the references.
reviewed by: T.S.S.R.K. Rao
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46A08
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46B40
zbMATH DE Number: 7358925
zbMATH Keywords: denting point
zbMATH Keywords: point of continuity
zbMATH Keywords: weak property \((\pi)\)
zbMATH Keywords: angle property
zbMATH Keywords: base for a cone
MaRDI profile type: Publication
full work available at URL: s13398-021-01054-y
OpenAlex ID: W3157088729
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DOI: 10.1007/S13398-021-01054-Y
description: scientific article; zbMATH DE number 7358925