Abstract: As applications of the parametric type of topologivally finite intaersection theorem in[1], a vector-valued minmax theorem in interval spaces is first proved and, some corollaries are obtained. Utilizing these results, some topological section theorems with their equivalent froms are obtained, and existence problems of Nash equilibria and Shafer-Sonneinschein equilibria for the abstract economies have been studied in this paper.

Key words: interval space, W-convex set, W-complete set, quasi-convex, equilibrium problem for abstract economy

摘要： 应用文[1]中得到的参数型拓扑有限交定理,首先证明了区间空间上向量值极大极小定理,并得到几个推论.作为应用,本文得到几个拓扑型截口定理及其等价形式,并研究了抽象经济Nash平衡和Shafer-Son-neinschein平衡存在问题.

关键词: 区间空间, W-凸集, W-紧集, 拟凸, 抽象, 经济平衡问题