Characterizations of weakly star-type Rothberger and Menger properties in hyperspaces

Abstract

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.