Countable sets, BCO spaces and selections
type: Item
instance of: scholarly article
title: Countable sets, BCO spaces and selections
zbMATH Open document ID: 1071.54009
author: Shouli Jiang
author: Peng-Fei Yan
published in: Topology and its Applications
publication date: 2005-03-08T00:00:00Z
review text: A base \({\mathfrak B}\) for a topological space \(X\) is called a base of countable order (BCO) if for every strictly decreasing sequence \(B_n\) of elements of \({\mathfrak B}\) containing \(x\), \(\{B_n: n= 1,2,\dots\}\) is a local base at \(x\). This paper is devoted to selections and multiselections of multifunctions taking values in BCO spaces (instead of metrizable). It is also proved that for a separable space \(X\), for each first countable space \(Y\) each multifunction \(F: X\to Y\) has a continuous selection if and only if \(X\) is countable.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 26E25
zbMATH DE Number: 2142276
zbMATH Keywords: multifunction
zbMATH Keywords: selection
zbMATH Keywords: countable sets
zbMATH Keywords: BCO spaces
zbMATH Keywords: based of countable order
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
full work available at URL: j.topol.2004.07.006
OpenAlex ID: W2018395157
cites work: Semi-continuous multifunctions and bases of countable order
cites work: Representing spaces as images of zero-dimensional spaces
cites work: Q3994935
cites work: Continuous selections. I
cites work: Continuous selections. II
cites work: A theorem on semi-continuous set-valued functions
cites work: Continuous selections and countable sets
cites work: Characterizations of Developable Topological Spaces
cites work: Q4392212
DOI: 10.1016/J.TOPOL.2004.07.006
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description: scientific article; zbMATH DE number 2142276