Examples concerning extensions of continuous functions
type: Item
instance of: scholarly article
title: Examples concerning extensions of continuous functions
zbMATH Open document ID: 1068.54019
author: Camillo Costantini
author: Dmitri Shakhmatov
published in: Topology and its Applications
publication date: 2004-10-01T00:00:00Z
review text: The problems connected with continuous extension of continuous functions are considered. A space \(X\) is called to be a total extender for given space \(Y\) provided that every continuous function defined on a subset of \(X\) with values in \(Y\) admits a continuous extension over \(X\). It is known that a space \(X\) is hereditarily extremally disconnected and hereditarily normal if and only if it is a total extender for every compact metrizable space \(Y\). In the paper under review it is shown that in the above statement one can not drop the hypothesis of metrizability of \(Y\) (leaving the assmption of compactness unchanged). However it is proved that a hereditarily extremally disconnected, hereditarily separable space \(X\) satisfying some stronger form of hereditary normality (so-called structural normality) is a total extender for every compact Hausdorff space. A non-trivial example of such an \(X\) is given.
reviewed by: A. A. Tolstonogov
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 2104480
zbMATH Keywords: extensions of continuous functions
zbMATH Keywords: hereditarily extremally disconnected space
zbMATH Keywords: total extender
zbMATH Keywords: forcing
MaRDI profile type: Publication
full work available at URL: j.topol.2004.02.016
OpenAlex ID: W2076469578
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DOI: 10.1016/J.TOPOL.2004.02.016
description: scientific article; zbMATH DE number 2104480