On compacta with convex projections
type: Item
instance of: scholarly article
title: On compacta with convex projections
zbMATH Open document ID: 0929.46013
DOI: 10.1016/S0166-8641(98)00053-4
author: Jan J. Dijkstra
author: Troy L. Goodsell
author: David G. Wright
published in: Topology and its Applications
publication date: 1999-09-13T00:00:00Z
review text: Let \(C\) be a convex subset of a convex \(n\)-dimensional compactum \(K\subset\mathbb{R}^n\). Assuming that \(C\) and \(K\) have the same projections on all linear subspaces of a fixed dimension \(k\) for \(0<k<n\), the authors prove that \(C\) contains a \((k-1)\)-sphere. If \(K\) is a polyhedron then \(C\) can be chosen of dimension \(k-1\). In the general case, \(C\) must contain a subset \(D\) of boundary points of \(K\) and can be chosen to equal \(DVZ\) where \(Z\) is a \(0\)-dimensional subset in the interior of \(K\).
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 57N15
zbMATH DE Number: 1317223
zbMATH Keywords: convex compactum
zbMATH Keywords: Euclidean \(n\)-space
zbMATH Keywords: Cantor set
zbMATH Keywords: projections
zbMATH Keywords: polyhedron
reviewed by: Yuri A. Brudnyi
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00053-4
OpenAlex ID: W2039525635
Recommended article: More on compacta with convex projections.
Recommended article: Convex compact spaces and their maps
Recommended article: ON CLOSED SETS WITH CONVEX PROJECTIONS
Recommended article: Q4558556
Recommended article: Compact convex sets and complex convexity
Recommended article: Compactification of strictly convex real projective structures
Recommended article: On compactness in locally convex spaces
Recommended article: Convex compactness and its applications
Recommended article: Condensations of projective sets onto compacta
Recommended article: Projections onto closed convex sets in Hilbert spaces
description: scientific article; zbMATH DE number 1317223