A fibration that does not accept two disjoint many-valued sections
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.
scientific article; zbMATH DE number 4178080