Topological properties of products of ordinals

Abstract

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.

Mild normality of finite products of subspaces of ω1

“…On the other hand recently, it has been known that strong zero-dimensionality behaves like mild normality in the realm of products of ordinals. In particular, without using elementary submodels, a simultaneous proof of strong zero-dimensionality and mild normality of products of arbitrary many ordinals is given in [5]. Moreover in the same paper, it is proved that Σ-products and σ -products of arbitrary many ordinals are both strongly zero-dimensional and mildly normal.…”