The hyperspace of hereditarily decomposable subcontinua of a cube is the Hurewicz set
type: Item
instance of: scholarly article
title: The hyperspace of hereditarily decomposable subcontinua of a cube is the Hurewicz set
zbMATH Open document ID: 1119.54009
author: Alicja Samulewicz
published in: Topology and its Applications
publication date: 2007-03-08T00:00:00Z
review text: It is shown that the hyperspace \(\mathcal{HD}(I^n)\) of hereditarily decomposable subcontinua of the cube \(I^n\) of finite or infinite dimension \(n\geq 3\) is an absorbing space for coanalytic spaces. Consequently, \(\mathcal{HD}(I^n)\) is homeomorphic to the Hurewicz space \(\mathcal{H}\) of all non-empty countable closed subsets in \([0,1]\). The same it true for the space \(\mathcal{DNP}(I^n)\) of decomposable subcontinua of \(I^n\) that contain no copy of the pseudoarc: \(\mathcal{DNP}(I^n)\) is homeomorphic to \(\mathcal H\).
reviewed by: Taras Banakh
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 57N20
zbMATH DE Number: 5131627
zbMATH Keywords: absorber
zbMATH Keywords: coanalytic set
zbMATH Keywords: continuum
zbMATH Keywords: hereditarily decomposable
zbMATH Keywords: pseudoarc
zbMATH Keywords: Hilbert cube
MaRDI profile type: Publication
full work available at URL: j.topol.2005.07.019
OpenAlex ID: W1991185767
cites work: Q4938163
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cites work: More non-analytic classes of continua
cites work: The pseudo-arc
cites work: Q3812929
DOI: 10.1016/J.TOPOL.2005.07.019
description: scientific article; zbMATH DE number 5131627