Selectively strongly star-menger spaces and related properties

A space X is selectively strongly star-Menger (briefly, selSSM) if for each sequence (Un : n ∈ N) of open covers of X and each sequence (Dn : n ∈ N) of dense subspaces of X, there exists a sequence (Fn : n ∈ N) of finite subsets Fn ⊂ Dn, n ∈ N, such that {st(Fn,Un): n ∈ N} is an open cover of X. This property is between absolute countable compactness [M. V. Matveev, Topol. Appl. 58, 81 (1994)] and selective absolute star-Lindelöfness [M. Bonanzinga et al., Topol. Appl. 221, 517 (2017)] and represents a “selective version” of the selection principle strongly star Menger [L. D. R. Kočinac, Publ. Math. Debrecen 55, 421 (1999)]. In this paper, we study some properties of selectively strongly star-Menger spaces, the relation with related properties and give some example distinguishing the properties considered.