Abstract
In this paper we characterize the Rothberger property and the selection principles star-Rothberger and strongly star-Rothberger in the hyperspaces CL(X), K(X), F(X) and CS(X), endowed with the Vietoris topology. To characterize the corresponding principles type star, we introduce a couple of technical selection principles, which we have denoted by SΠV(ΠV(Λ),ΠV(Λ)) and SΠV⁎(ΠV(Λ),ΠV(Λ)). Also, we give an equivalence of the selection principle S1(D,D) in the same hyperspaces, by using cV-covers of a space.
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