关键词: 区间空间, W-凸集, W-紧集, 拟凸, 抽象, 经济平衡问题

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