Remarks on Pseudo-continuity

TL;DR

This paper extends a maximum theorem, explores minimax inequalities related to Ky Fan's theorem, and shows the equivalence of Nash equilibrium existence results to classical theorems, contributing to mathematical optimization theory.

Contribution

It extends Morgan and Scalzo's maximum theorem, links minimax inequalities to Ky Fan's theorem, and clarifies the equivalence of Nash equilibrium existence to classical results.

Findings

Extended Morgan and Scalzo's maximum theorem.

Established equivalence between minimax inequalities and Ky Fan's theorem.

Proved Nash equilibrium existence result is equivalent to a classical theorem.

Abstract

In this work we extend a maximum theorem proposed by Morgan and Scalzo. We also show some results of minimax inequalities which are equivalent to the famous Ky Fan minimax inequality. Additionally, we prove that the existence result of Nash equilibria proposed by Morgan and Scalzo is actually equivalent to a classical result in the literature.