Note on hereditary normality of product spaces
Paracompact spaces \(X\) are constructed that are weak \(P(\omega)\) but not \(P(\omega)\), i.e., \(X\times Y\) is paracompact for every \(K\)-analytic space \(Y\), and not normal for some separable metrizable \(Y\). It is proved for a separable metrizable \(X\) that \(X\times Y\) is hereditarily normal for every hereditarily normal weak \(P(\omega)\)-space \(Y\) iff \(X\) is countable. In connection with the above results, the following problem is posed: In order that \(X\times Y\) be normal for any normal weak \(P(\omega)\)-space \(Y\), is it necessary that \(X\) be a \(K\)-analytic space?
scientific article; zbMATH DE number 1121473