Base-normality and product spaces

We introduce the notion of base-normality, which is a natural generalization of base-paracompactness introduced by J.E. Porter. We prove the following: (1) For a base-normal space X and a metrizable space Y, the product space X × Y is normal if and only if X × Y is base-normal. (2) For the countable product X = ∏ i ∈ N X i of spaces X i such that finite subproducts ∏ i ⩽ n X i , n ∈ N , are base-normal, X is normal if and only if X is base-normal. (3) Every Σ-product of metric spaces is base-normal. Many applications for analogue of classical theorems on normality of products are also given.