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 Σ-products of ordinals are quasi-perfect preimages of Σ-products of copies of ω. We obtain as corollaries that products of ordinals are κ-normal and strongly zero-dimensional. Also, σ-products and Σ-products of ordinals are shown to be countably paracompact, κ-normal and strongly zero-dimensional. Normality in Σ-products and σ-products of ordinals is also characterized. It is also shown that any continuous real-valued function on a σ-product of ordinals has countable range.