The quasi-Rothberger property of Pixley-Roy hyperspaces

Let PR(X) denote the hyperspace of non-empty finite subsets a topological space X with Pixley-Roy topology. In this paper, we investigate quasi-Rothberger property in PR(X). We prove that for X, followings are equivalent: (1) is quasi-Rothberger; (2) satisfies S1(?rc f?h,?wrc f?h); (3) separable and each co-finite subset S1(?pc f?h,?wpc (4) PR(Y) Y X. also characterize quasi-Menger quasi-Hurewicz These answer questions posted [8].