On the different kinds of separability of the space of Borel functions

Abstract In paper we prove that: a space of Borel functions B(X) on a set of reals X, with pointwise topology, to be countably selective sequentially separable if and only if X has the property S 1(BΓ , BΓ ); there exists a consistent example of sequentially separable selectively separable space which is not selective sequentially separable. This is an answer to the question of A. Bella, M. Bonanzinga and M. Matveev; there is a consistent example of a compact T 2 sequentially separable space which is not selective sequentially separable. This is an answer to the question of A. Bella and C. Costantini; min{𝔟, 𝔮} = {κ : 2 κ is not selective sequentially separable}. This is a partial answer to the question of A. Bella, M. Bonanzinga and M. Matveev.