A fibration that does not accept two disjoint many-valued sections (Q752523)
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scientific article; zbMATH DE number 4178080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fibration that does not accept two disjoint many-valued sections |
scientific article; zbMATH DE number 4178080 |
Statements
A fibration that does not accept two disjoint many-valued sections (English)
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1990
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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.
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open map
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fibration
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multivalued section
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1-soft map
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