Remarks on selectively (a)-spaces

In this paper, we continue to study the versions of property (a), and show the following statements:(1)There exists a Tychonoff countably compact space X such that AD(X) is selectively (a), but X is not selectively (a);(2)There exists a Tychonoff selectively (a)-space X having a regular-closed subspace which is not selectively (a);(3)Assuming 2ℵ0=2ℵ1, there exists a normal space X that is not selectively (a);(4)If X is a normal selectively (a)-space with e(X)<ω1, then AD(X) is selectively (a).The statement (1) answers negatively Caserta, Di Maio and Kočinac (2011) [1, Question 2.11].