Admissible fibers and \(T\)-admissibility in hyperspaces
type: Item
instance of: scholarly article
title: Admissible fibers and \(T\)-admissibility in hyperspaces
zbMATH Open document ID: 0826.54005
DOI: 10.1016/0166-8641(95)00084-T
author: Choon Jai Rhee
published in: Topology and its Applications
publication date: 1995-09-04T00:00:00Z
review text: Let \(X\) be a metric continuum. Denote by \(2^X\) and \(C(X)\) the hyperspaces of all nonempty closed subsets and all nonempty subcontinua of \(X\), respectively. The space \(X\) is said to be \(T\)-admissible if it admits a Whitney map \(\mu : C(X) \to [0, \mu(X)]\) having some special properties that are too technical to repeat in this review. It is known that hyperspace contractibility for \(X\) implies \(T\)-admissibility for \(X\). In this interesting paper the author proves among other things that \(X\) is \(T\)-admissible if and only if \(C(X)\) is \(T\)-admissible. He also presents an example of a \(T\)-admissible continuum \(X\) such that \(C(X)\) is not contractible. As a consequence, \(C(X)\) is \(T\)-admissible and therefore does not contain any \(R^i\)-continuum. This answers a question of Charatonik.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 792532
zbMATH Keywords: metric continuum
zbMATH Keywords: subcontinua
zbMATH Keywords: Whitney map
zbMATH Keywords: hyperspace contractibility
zbMATH Keywords: \(T\)-admissibility
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 792532