In this paper, we introduce the selection principles wSS* 1(??(?),C?(?)),
wSS* fin(??(?),C?(?)), wS* 1(??(?),C?(?)) and wS* fin(??(?),C?(?)) to
characterize the properties of weakly strong-star Rothberger (Menger) and
weakly star-Rothberger (Menger) in the hyperspace (?, ?+ ?), respectively.
Furthermore, we introduce the notions H(C?(?)) and Ifin(C?(?),C?(?)) to
characterize, respectively, the H-separability and the principle Ufin(D,D),
in the same hyperspace.