Star versions of the Rothberger property on hyperspaces

摘要

We introduce the notion of pi(F)(Delta)-network and denote the combinatorial principles FELL(11(F)(Delta),11(F)(Delta)) and FELL*(11(F)(Delta), 11(F)(Delta)), which will be applied to characterize the spaces X whose hyperspace, endowed with the Fell topology, satisfies the SSR condition and the SR condition. We use the selection principle SS Delta* (O,O) to characterize the SSR property for the spaces K(X), F(X) and [X](1), endowed with the lower Vietoris topology. In addition, we introduce the selection principle S-Delta f (O,O) to obtain characterizations of the selective versions of metacompactness, mesocompactness and sequential mesocompactness. Finally, we introduce the notion of Delta-moving-off family, which generalizes the one of moving-off family, and we use it to characterize the Rothberger property for certain subspaces of CL(X). (C) 2020 Elsevier B.V. All rights reserved.