Infinite products of quasi-continuous functions
type: Item
instance of: scholarly article
title: Infinite products of quasi-continuous functions
zbMATH Open document ID: 1185.54013
author: Katarzyna Chmielewska
author: Aleksander Maliszewski
published in: Topology and its Applications
publication date: 2009-11-05T00:00:00Z
review text: Recall that a function \(f:X\to Y\) between topological spaces is \textit{quasi-continuous} provided \(f^{-1}(V)\subset\overline{\text{Int}(f^{-1}(V))}\) for each open \(V\subset Y\). It is shown that a function \(f:X\to\mathbb R\), where \(X\) is metric, is an infinite product of a sequence of quasi-continuous functions if and only if \(f\) is a Baire function and \(\overline{f^{-1}(0,\infty)}\cap\overline{f^{-1}(-\infty,0)}\setminus f^{-1}(0)\) is meagre. Consequently a cliquish function \(X\to\mathbb R\), \(X\) metric, is such a product.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 5625510
zbMATH Keywords: Baire property
zbMATH Keywords: cliquishness
zbMATH Keywords: quasi-continuity
zbMATH Keywords: infinite product of functions
MaRDI profile type: Publication
full work available at URL: j.topol.2009.03.048
OpenAlex ID: W1996808040
cites work: Limits of simply continuous functions
cites work: Sums of quasicontinuous functions defined on pseudometrizable spaces
cites work: Infinite products of Borel measurable functions
cites work: Types of Functions
DOI: 10.1016/J.TOPOL.2009.03.048
description: scientific article; zbMATH DE number 5625510