Sequential + separable vs sequentially separable and another variation on selective separability (Q1939371)

A topological space \(X\) is sequentially separable if \(X\) has a countable dense subset \(D\) such that every point of \(X\) is the limit of a sequence of points from \(D\), see \textit{F. D. Tall} [Proc. Am. Math. Soc. 46, 310--314 (1974; Zbl 0268.54006)]. The class of sequentially separable spaces includes all strongly sequentially separable spaces (hence all separable Fréchet spaces) and \(M\)-sequentially separable spaces [the authors, Topology Appl. 157, No. 15, 2389--2391 (2010; Zbl 1197.54038)]. The authors present an example of a separable and sequential space which is not sequentially separable. Also, they give an example of a sequentially separable space which is neither strongly sequentially separable nor sequential. They investigate some conditions for which sequential+separable is sequentially separable and vice versa.