H-star-Lindelöf property and weaker versions

Abstract

We introduce the selection principles H-star-Lindelöf, weakly H-star-Lindelöf and almost H-star-Lindelöf and we provide some propositions and relationships with other known properties in literature. Furthermore, in this paper we characterize the above selection principles in hyperspaces endowed with the hit-and-miss topology ${\tau }_{\Delta }$, by using a new property ${\mathrm{SS}}_{{\Pi }_{\Delta }\left(\Lambda \right),\text{fin}}^{\star }\left(C_{\Delta }\right(\Lambda ),B)$, for the corresponding choose of the family $B$.