Continuous functions on compact totally ordered spaces
type: Item
instance of: scholarly article
title: Continuous functions on compact totally ordered spaces
zbMATH Open document ID: 0871.54022
author: J. E. Jayne
author: C. A. Rogers
author: Isaac Namioka
published in: Journal of Functional Analysis
publication date: 1997-10-05T00:00:00Z
review text: The authors prove that for any compact linearly ordered space \(K\), the space \(C_p(K)\) of continuous functions on \(K\) endowed with the topology of pointwise convergence is \(\sigma\)-fragmented using closed sets. The notion of \(\sigma\)-fragmentability was introduced by the same authors in [Mathematika 39, No. 1, 161-188 (1992; Zbl 0761.46008), No. 2, 197-215 (1992; Zbl 0761.46009)], where this was used to study various properties of (dual) Banach spaces. The above theorem combined with some results of Cornett, Pearson, van Mill and Wattel, and of Nikiel implies that \(C_p(K)\) is \(\sigma\)-fragmented when \(K\) is a dendron or a compact space with a closed crossfree subbase for its topology.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 850621
zbMATH Keywords: dual space
zbMATH Keywords: linearly ordered space
zbMATH Keywords: dendron
reviewed by: Mikhail Tkachenko
MaRDI profile type: Publication
full work available at URL: jfan.1995.1145
OpenAlex ID: W1978684501
DOI: 10.1006/JFAN.1995.1145
description: scientific article; zbMATH DE number 850621