Selection principles of the Fell topology and the Vietoris topology

Let CL(X)CL(X) denote the set of all nonempty closed subsets of a topological space X  . In this paper, we introduce the definitions of kFkF-covers and cVcV-covers of X  . Under Fell topology τFτF and Vietoris topology τVτV on CL(X)CL(X), we investigate the following selection principles: Rothberger properties, Menger properties and Hurewicz properties, and also characterize tightness-like covering properties: tightness, Set-tightness and T-tightness.