On the D-property of certain products

We first point out that the product of a subparacompact DCDC-like space and a subparacompact D-space is a D  -space. As a main result, we use elementary submodels to prove that any countable product of subparacompact DCDC-like spaces is a D  -space. More generally, we prove that any uncountable product of subparacompact DCDC-like spaces is a D-space if and only if all but countably many of the factors are compact.