非紧空间及一般点集上极大极小定理

Minimax Theorems in Topological Spaces Without Compact and Arbitrary Sets

给出了一类非紧空间及一般点集上极大极小定理，首先证明了，Ｘ为拓扑空间，Ｙ为任意集时，具有ｔ－拟凸性的泛函ｆ，ｇ：Ｘ×Ｙ→Ｒ的极大极小比较定理。其次证明了，Ｘ和Ｙ均为任意集时，具有ｔ－拟凸性的殆周期泛函ｆ的极大极小定理。

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.