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 τΔ, by using a new property SSΠΔ(Λ),fin⋆(CΔ(Λ),B), for the corresponding choose of the family B.
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