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The main result of the paper is a series of theorems, called here Infimum Principles. As applications, we derive some well-known results related to fixed point, minimax, and equilibrium theorems including the Nash equilibrium theorem and Gale-Nikaido theorem. Our study is based on and utilizes the techniques of simplicial structures and CO families. This approach enables us to derive not only classical theorems but also stimulates new research.