\(\varSigma\)-products of paracompact \(C\)-scattered spaces (Q1862038)

The main result of the paper is that every \(\Sigma\)-product of paracompact \(C\)-scattered spaces is (collectionwise) normal if it has countable tightness. Thus the paper completes a number of well-known results related to the normality of \(\Sigma\)-products obtained by various authors over the years. The new aspect of the authors' approach is in the combination of the \(\Sigma\) product with the concept of \(C\)-scattered spaces (which was introduced by Telgársky in the 70's) for which several new ideas and techniques were developed in the paper. The paper is closed by two open questions: (1) Let \(\Sigma\) be a \(\Sigma\)-product of paracompact \(C\)-scattered spaces. Is \(\Sigma\) collectionwise normal if it is normal? (2) Let \(\Sigma\) be a \(\Sigma\)-product of paracompact \(C\)-scattered spaces. Is \(\Sigma\) shrinking (equivalently, subshrinking) if it has countable tightness?