Remarks on selectively (a)-spaces

Abstract: 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 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 , there exists a normal space X that is not selectively (a); [(4)] If X is a normal selectively (a)-space with , then is selectively (a). The statement (1) answers negatively Caserta, Di Maio and Kočinac (2011) [1, Question 2.11]. [Copyright &y& Elsevier]