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.
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This research was partially supported by FONDECYT Project 1200525.
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Communicated by Sergey Zhukovskiy.
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Fierro, R. An Intersection Theorem for Topological Vector Spaces and Applications. J Optim Theory Appl 191, 118–133 (2021). https://doi.org/10.1007/s10957-021-01927-7
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DOI: https://doi.org/10.1007/s10957-021-01927-7