Maurice Sion proved a general minimax theorem in 1958. The theorem applies to functions that are quasi-concave-convex and appropriately semi-continuous in each variable. The result unifies two approaches to minimax theorems: one using separation of convex sets and another using fixed point theorems. The key tool in the proof is a theorem by Knaster, Kuratowski, and Mazurkiewicz based on Sperner's lemma. The paper introduces definitions of concave-like, convex-like, quasi-concave, quasi-convex, and quasi-concave-convex functions. It then presents several theorems and lemmas that support the main result. The main theorem states that for convex, compact spaces M and N, and a function f that is quasi-concave-convex and u.s.c.-l.s.c., the supremum of the infimum of f equals the infimum of the supremum of f. This result is shown to be a generalization of von Neumann's minimax theorem and other related results. The paper also discusses the importance of topological conditions such as compactness and semi-continuity in the minimax theorems. It provides an example showing that the u.s.c.-l.s.c. condition cannot be removed or significantly weakened even for finite-dimensional spaces. The paper concludes by discussing minimax theorems for concave-convexlike functions, which are shown to be special cases of the main theorem.Maurice Sion proved a general minimax theorem in 1958. The theorem applies to functions that are quasi-concave-convex and appropriately semi-continuous in each variable. The result unifies two approaches to minimax theorems: one using separation of convex sets and another using fixed point theorems. The key tool in the proof is a theorem by Knaster, Kuratowski, and Mazurkiewicz based on Sperner's lemma. The paper introduces definitions of concave-like, convex-like, quasi-concave, quasi-convex, and quasi-concave-convex functions. It then presents several theorems and lemmas that support the main result. The main theorem states that for convex, compact spaces M and N, and a function f that is quasi-concave-convex and u.s.c.-l.s.c., the supremum of the infimum of f equals the infimum of the supremum of f. This result is shown to be a generalization of von Neumann's minimax theorem and other related results. The paper also discusses the importance of topological conditions such as compactness and semi-continuity in the minimax theorems. It provides an example showing that the u.s.c.-l.s.c. condition cannot be removed or significantly weakened even for finite-dimensional spaces. The paper concludes by discussing minimax theorems for concave-convexlike functions, which are shown to be special cases of the main theorem.