Saddle points in completely regular topological spaces

TL;DR

This paper characterizes completely regular topological spaces and establishes a variational principle for saddle points within these spaces, also examining the well-posedness of such problems.

Contribution

It introduces a new variational principle for saddle points in completely regular topological spaces and analyzes their well-posedness.

Findings

Characterization of completely regular topological spaces

Establishment of a variational principle for saddle points

Analysis of well-posedness of saddle point problems

Abstract

We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle point problems is studied as well.