Span of subcontinua
type: Item
instance of: scholarly article
zbMATH Open document ID: 1276.54026
author: Nadeeka De Silva
publication date: 2013-09-27T00:00:00Z
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 6212859
zbMATH Keywords: continuum
zbMATH Keywords: ray
zbMATH Keywords: span
zbMATH Keywords: semispan
zbMATH Keywords: subcontinuum
zbMATH Keywords: surjective span
MaRDI profile type: Publication
title: Span of subcontinua
published in: Topology Proceedings
review text: The paper under review considers span of a ray \(Y\) limiting to a continuum \(X\). Note that if \(X\) is a simple closed curve then its span is the same as the span of \(Y\). The author proves a somewhat intuitive estimate for cases when \(X\) is not a simple closed curve. Namely, the span of \(Y\) does not exceed the span of \(X\) or the surjective semispan of \(X\), whichever is bigger. Building on the work of \textit{Z. Waraszkiewicz} [``Une famille indenombrable de continus plans dont aucun n'est l'image continue d'un autre'', Fundamenta 18, 118--137 (1932; JFM 58.0632.02)] the author demonstrates the existence of an uncountable family of pairwise incomparable continua for each member of which the set of values of spans of its subcontinua coincides with the Cantor set. A similar result is obtained when the Cantor set is replaced by an arbitrary closed subset of [0,1] containing 0 and 1.
reviewed by: K. T. Hallenbeck
description: scientific article; zbMATH DE number 6212859