Topological properties of products of ordinals (Q1880721)

The paper deals with \(\Sigma\) and \(\sigma\)-products of spaces (or subspaces) of ordinals. It is proved that such \(\Sigma\)-products are quasi-perfect preimages of \(\Sigma\)-products of countable discrete spaces and, thus, are countably paracompact and \(\omega_1\)-compact, and normality of such \(\Sigma\)-products is characterized (more is proved when one takes the subspaces of ordinals with at most countable cofinality). As for \(\sigma\)-products of ordinals (with the base point 0), they are countably paracompact, \(\kappa\)-normal and strongly zero-dimensional; they are normal iff every finite subproduct is normal.