Continuous functions that are locally constant on dense sets
type: Item
instance of: scholarly article
title: Continuous functions that are locally constant on dense sets
zbMATH Open document ID: 0916.46019
author: Mary Ellen Rudin
author: Walter Rudin
published in: Journal of Functional Analysis
publication date: 1996-03-04T00:00:00Z
review text: For a space \(X\), let \(E_0(X)\) be the family of all continuous real-valued functions on \(X\) that are locally constant on a dense (open) subset of \(X\). It was a question of S. Sidney whether \(E_0(X)\) always separates points of \(X\) for a compact Hausdorff space \(X\). The authors present an example of a path-connected compact Hausdorff space \(X\) which answers Sidney's question in the negative.
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 850604
zbMATH Keywords: locally constant on a dense (open) subset
zbMATH Keywords: separates points
zbMATH Keywords: path-connected compact Hausdorff space
reviewed by: Mikhail Tkachenko
Wikidata QID: Q101069368
MaRDI profile type: Publication
full work available at URL: jfan.1995.1121
OpenAlex ID: W2064886506
DOI: 10.1006/JFAN.1995.1121
description: scientific article; zbMATH DE number 850604