一般化凸空间上的一个连续选择定理

摘要

本文研究一般化凸空间上的连续选择定理.利用在D(C)的条件下,一般化凸空间(X,D；Γ)上(Γ)-凸子集的概念,得到了两类一般化凸空间之间,以及φ映射和(Γ)-凸映射之间的关系,并且得到了一个连续选择定理.本文推广了一般化凸空间上凸子集的概念.%In this artilce,we discuss a continuous selection theorem on generalized convex space.Using the definition of (Γ)-convex set in a generalized convex space (X,D; Γ),where D is not necessarily a subset of X,we get the relationship between generalized convex spaces with D (C) X and generalized convex spaces with D (C) X,as well as the relationship between φ-map and a multimap with nonempty (Γ)-convex values.Moreover,we also get a continuous selection theorem.We extend the conception of (Γ)-convex set in the generalized convex space.