Selection principles in hyperspaces with generalized Vietoris topologies

We continue investigations of Čech closure spaces and their hyperspaces started in [M. Mršević, M. Jelić, Selection principles and hyperspace topologies in closure spaces, J. Korean Math. Soc. 43 (2006) 1099–1114] and [M. Mršević, M. Jelić, Selection principles, γ-sets and αi-properties in Čech closure spaces, Topology Appl., in press], focusing on generalized upper and lower Vietoris topologies.