Abstract
We investigate a selective version of property (a) and prove a number of results showing that, under certain set theoretical conditions, (a) spaces and selectively (a) spaces behave in a very similar way, at least for separable spaces. Several results regarding the presence of the referred selective version in spaces from almost disjoint families are established; in particular, we give a combinatorial characterization of such presence. Consistent set theoretical hypotheses implying equivalence between being (a) and being selectively (a) within the referred class are presented, as well as hypotheses implying non-equivalence. We also show that the Continuum Hypothesis is independent of the statement asserting the above mentioned equivalence. The paper finishes by presenting some notes and questions on the role of set theoretical assumptions in the subject.
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