Topological properties of products of ordinals

We study separation and covering properties of special subspaces of products of ordinals. In particular, it is proven that certain subspaces of Sigma-products of ordinals are quasi-perfect preimages of Sigma-products of copies of omega. We obtain as corollaries that products of ordinals are kappa-normal and strongly zero-dimensional. Also, sigma-products and Sigma-products of ordinals are shown to be countably paracompact, kappa-normal and strongly zero-dimensional. Normality in Sigma-products and sigma-products of ordinals is also characterized. It is also shown that any continuous real-valued function on a sigma-product of ordinals has countable range. (C) 2004 Elsevier B.V. All rights reserved.