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An Intersection Theorem for Topological Vector Spaces and Applications

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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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Acknowledgements

This research was partially supported by FONDECYT Project 1200525.

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  1. Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Raúl Fierro

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  1. Raúl Fierro
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Correspondence to Raúl Fierro.

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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

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