Rothberger and Rothberger-type star selection principles on hyperspaces

摘要

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 S Pi V (Pi(V) (Lambda), Pi(V) (Lambda)) and S-Pi V* (Pi(V)(Lambda), Pi(V) (Lambda)). Also, we give an equivalence of the selection principle S1(D,D) in the same hyperspaces, by using cV-covers of a space. (C) 2020 Elsevier B.V. All rights reserved.