On convex cones with Schwarz-Zamfirescu property
type: Item
instance of: scholarly article
title: On convex cones with Schwarz-Zamfirescu property
zbMATH Open document ID: 0931.52001
DOI: 10.1007/BF02463343
publication date: 1999-05-27T00:00:00Z
review text: The author proves that most points of a typical compact convex subset of a locally compact infinite-dimensional metric one are extreme points. As usual, ``most'' means all except of those in a set of first Baire category, and by ``typical set'' we mean a set whose complement is a union of a countable family of nowhere dense sets. The presented theorem is analogical to the result of \textit{T. Schwarz} and \textit{T. Zamfirescu} [J. Austral. Math. Soc., Ser. A 43, 287-290 (1987; Zbl 0629.52002)].
Mathematics Subject Classification ID: 52A05
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 1292503
zbMATH Keywords: Hausdorff metric
zbMATH Keywords: convex cones
zbMATH Keywords: extreme points
zbMATH Keywords: Baire category
author: Efim M. Bronshteĭn
reviewed by: Marek Lassak
MaRDI profile type: Publication
cites work: Some new results on smoothness and rotundity in normed linear spaces
cites work: Q5508589
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1292503