Normality and closed projections of products with a cardinal factor
Let \(X\) be a normal space and let \(\kappa\) denote the space of ordinal numbers less than the initial ordinal of a regular cardinal \(\kappa\). The authors discuss the relationship between the following two conditions: (a) the product space \(X\times \kappa\) is normal; (b) the projection \(\pi_X: X\times \kappa\to X\) is a closed map. In particular, it is proved that if \(X\) is either \(<\kappa\)-paracompact and \(\kappa\)-compact or a \(<\kappa\)-paracompact GO-space, then (a) and (b) are equivalent. An example is given showing that there is a paracompact space \(X\) satisfying (a) but not (b).
scientific article; zbMATH DE number 896596