Minimax Theorems in Topological Spaces Without Compact and Arbitrary Sets

In this paper,we give minimax theorems in topological spaces without compact and arbitrary sets. First,we prove a minimax inequality for t-convexlike function f and g on the product set X×Y of a topological space X and an arbitrary set Y.Secondly, we prove a minimax theorem for t-convexlike almost periodic function f on the product set X×Y of two arbitrary sets X and Y.