Investigating the tightness of (CL(X), TF+) using elementary submodels.
D. Di Caprio

In the paper, Tightness, character and related properties of hyperspace topologies, Costantini, Holá and Vitolo prove that the hypothesis of regularity for the base space X is sufficient to produce the following limitation for the tightness of the upper Fell Topology, t_F+, on the set of all closed subsets of X: (CL(X),t_F+) <= g(X)hL(X), where g(X) is min{m : X has a complete m-system}. We investigate when an elementary submodel contains a base or pseudobase at a compact set and obtain the above bound on tightness as an immediate consequence.