Convex Hilbert cubes in superextensions
type: Item
instance of: scholarly article
title: Convex Hilbert cubes in superextensions
zbMATH Open document ID: 0588.54026
DOI: 10.1016/0166-8641(86)90024-6
author: Marcel van de Vel
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: Let X be a metrizable continuum. The superextension \(\lambda\) X of X is the space of all maximal linked systems of closed subsets of X equipped with a natural Wallman topology. It is known that \(\lambda\) X is homeomorphic to the Hilbert cube [see \textit{J. van Mill}, Fundam. Math. 107, 201-224 (1980; Zbl 0449.54024)]. Superextensions carry a natural convex structure. The author proves that each nondegenerate compact convex subset of \(\lambda\) X is homeomorphic to the Hilbert cube, thereby extending the reviewer's result in a nontrivial way.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 52A01
zbMATH DE Number: 3944814
zbMATH Keywords: selection
zbMATH Keywords: metrizable convex structure
zbMATH Keywords: superextension
zbMATH Keywords: maximal linked systems of closed subsets
zbMATH Keywords: Wallman topology
zbMATH Keywords: nondegenerate compact convex subset
zbMATH Keywords: Hilbert cube
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90024-6
OpenAlex ID: W2124793791
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description: scientific article; zbMATH DE number 3944814