Function spaces which are stratifiable
type: Item
instance of: scholarly article
title: Function spaces which are stratifiable
zbMATH Open document ID: 0832.54026
author: Bao-Lin Guo
published in: Tsukuba Journal of Mathematics
publication date: 1996-03-05T00:00:00Z
review text: It is well-known that if \(X\) is a compact metric and \(Y\) a stratifiable space, \(C(X,Y)\) with the compact-open topology may fail to be stratifiable. The following is proved here. Theorem: Let \(X\) be a compact metric space which has a \(\sigma\)-\(CP\)-\(CF\) quasi-base consisting of closed sets. Then \(C(X,Y)\) has a \(\sigma\)-\(CP\) quasi-base; hence, it is stratifiable. Example: If \(X = \{0\} \cup \{{1 \over n} |n = 1,2, \ldots\}\) is the space of a convergent sequence there exists a countable Lashnev space \(Y\) such that \(C(X,Y)\) is not stratifiable.
Mathematics Subject Classification ID: 54E20
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 729225
zbMATH Keywords: \(CP\)-quasi-base
zbMATH Keywords: \(CF\)-quasi-base
zbMATH Keywords: stratifiable space
reviewed by: Carlos R. Borges
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162617
OpenAlex ID: W343891162
DOI: 10.21099/TKBJM/1496162617
description: scientific article; zbMATH DE number 729225