A direct proof of a theorem on monotonically normal spaces for GO-spaces
\textit{Z. Balogh} and \textit{M. E. Rudin} have proved in [Topology Appl. 47, No. 2, 115--127 (1992; Zbl 0769.54022)] that any monotonically normal space \(X\) has the following property: Every open cover of \(X\) has a \(\sigma\)-disjoint open partial refinement \(\mathcal V\) such that \(X\setminus \cup{\mathcal V}\) is the union of a discrete family of closed subspaces which are homeomorphic to some stationary subset of a regular uncountable cardinal. In particular, since any GO-space is monotonically normal, GO-spaces have this property. In the present paper the author gives a direct proof of this fact.
scientific article; zbMATH DE number 5652738
scientific article