D-spaces, aD-spaces and finite unions

In this paper, we prove that if a space X is the union of a finite family of strong Σ-spaces, then X is a D-space. This gives a positive answer to a question posed by Arhangelʹskii in [A.V. Arhangelʹskii, D-spaces and finite unions, Proc. Amer. Math. Soc. 132 (2004) 2163–2170]. We also obtain results on aD-spaces and finite unions. These results improve the correspond results in [A.V. Arhangelʹskii, R.Z. Buzyakova, Addition theorems and D-spaces, Comment. Math. Univ. Carolin. 43 (2002) 653–663] and [Liang-Xue Peng, The D-property of some Lindelöf spaces and related conclusions, Topology Appl. 154 (2007) 469–475].