The structure of locally compact normal spaces: some quasi-perfect preimages
With \(W_0\subset\omega_1\) the set of isolated points and \(E\subset\omega_1\) any stationary, co-stationary subset containing \(W_0\), a locally compact, normal topology is constructed on \(X=W_0\cup[(E\setminus W_0)\times\mathfrak b]\) such that the projection \(\pi:X\to E\) is a quasi-perfect map. For each \(\alpha\in E\setminus W_0\), the fibre \(\pi^{-1}(\alpha)\) is homeomorphic to \(\mathfrak b\) with the usual topology and \(X\) is locally countable if and only if \(\mathfrak b=\omega_1\). The restriction \(W_0\subset E\) may be removed.
scientific article; zbMATH DE number 6710339