A fibration that does not accept two disjoint many-valued sections
type: Item
instance of: scholarly article
title: A fibration that does not accept two disjoint many-valued sections
zbMATH Open document ID: 0715.54006
DOI: 10.1016/0166-8641(90)90121-H
published in: Topology and its Applications
publication date: 1990-01-01T00:00:00Z
review text: In the ``Continuum theory problems - update'', collected by \textit{W. Lewis} in Topology Proc. 9, 374-382 (1984; Zbl 0576.54002),there is the following (166) due to \textit{W. Bula}. Suppose \(f:X\to Y\) is an open mapping, with each of X and Y compact metric and each \(f^{-1}(y)\) infinite. Do there exist disjoint closed subsets F and H of X such that \(f(F)=f(H)=Y?\) The author presents a negative answer to this question under an essential assumption that the range space Y is infinite- dimensional. Some further questions in the area are asked.
reviewed by: Janusz J. Charatonik
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 55R25
zbMATH DE Number: 4178080
zbMATH Keywords: open map
zbMATH Keywords: fibration
zbMATH Keywords: multivalued section
zbMATH Keywords: 1-soft map
author: Alexander Dranishnikov
MaRDI profile type: Publication
cites work: Q3799335
cites work: Q3333698
cites work: Q3697776
cites work: Continuous selections. II
cites work: Characteristic Classes. (AM-76)
description: scientific article; zbMATH DE number 4178080