On weaker versions of R-star-Lindelöf and M-star-Lindelöf properties

Abstract

In this paper, we introduce and analyze the selection principles weakly (almost) R-star-Lindel\"of and weakly (almost) M-star-Lindel\"of, which turn out to be weaker versions of the R-star-Lindel\"of and M-star-Lindel\"of properties, respectively, and we provide some relationships with other known properties in literature. Also, we introduce the selection principles $\mathbf{SS}_{\Pi_{\Delta}(\Lambda),1}^{\star}(\mathbb{C}_{\Delta}(\Lambda), \mathscr{B})$ and $\mathbf{SS}_{\Pi_{\Delta}(\Lambda),\textsf{fin}}^{\star}(\mathbb{C}_{\Delta}(\Lambda), \mathscr{B})$ to characterize the properties weakly (almost) R-star-Lindel\"of and weakly (almost) M-star-Lindel\"of in the hyperspace $(\Lambda,\tau_{\Delta}^+)$, respectively.