The smallest subring of the ring \(C_ p(C_ p(X))\) containing X\(\cup \{1\}\) is everywhere dense in \(C_ p(C_ p(X))\)
type: Item
instance of: scholarly article
title: The smallest subring of the ring \(C_ p(C_ p(X))\) containing X\(\cup \{1\}\) is everywhere dense in \(C_ p(C_ p(X))\)
zbMATH Open document ID: 0624.54015
published in: Moscow University Mathematics Bulletin
publication date: 1987-01-01T00:00:00Z
review text: A Tikhonov space X is called k-separable if it contains a dense countable union of compact sets. It is shown that if X is k-separable then so is \(C_ p(C_ p(X))\) (the converse is not true). This result follows from the following one: If \(Y\subset X\) then the smallest ring in \(C_ p(C_ p(X))\) containing Y and all constant functions is dense in \(C_ p(C_ p(X))\) iff Y is dense in X.
reviewed by: M. Hušek
Mathematics Subject Classification ID: 54C40
zbMATH DE Number: 4013509
zbMATH Keywords: k-separable space
author: Vladimir Tkachuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4013509