Abstract

We extend, to the framework of topological vector spaces, two results by Horvath and Kuratowski related to conditions for a family of closed sets to have compact and nonempty intersection. This extension enables us to introduce a number of applications such as the existence of maximal elements in preordered spaces, issues related to KKM functions, fixed point theorems, a variant of a matching theorem by Fan, and mainly the improvement of some minimax and variational inequalities.