Almost strongly star-Menger and related properties

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In this paper we introduce the almost strongly star-Menger property and we provide some results and relationships with another known properties in literature. Furthermore, we characterize the almost strongly star-Menger and the almost star-Menger properties in hyperspaces endowed with the hit-and-miss topology $\tau_\Delta$, by using two new selection principles $\mathbf{S}_{\textsf{fin}}^{\star}(\Pi_{\Delta}(\Lambda), \mathscr{B})$ and $\mathbf{SS}_{\textsf{fin}}^{\star}(\Pi_{\Delta}(\Lambda), \mathscr{B})$, for an appropriate family $\mathscr{B}$.