论文标题
准点可分离的拓扑矢量空间的固定点特性
The Fixed Point Property of Quasi-Point-Separable Topological Vector Spaces
论文作者
论文摘要
在本文中，我们介绍了准点可分离的拓扑矢量空间的概念，该拓扑矢量空间具有以下重要属性：1。总的来说，拓扑矢量空间是准点 - 分离的条件并不难检查； 2.类准点可分离的拓扑矢量空间非常大，其中包括局部凸拓扑矢量空间和伪型伴随拓扑矢量空间作为特殊情况； 3.每一个准点分离的休斯都拓扑矢量空间具有固定点属性（即，在任何给定的非空封闭且凸子集的每个连续自映射具有固定点），这是本文主定理的结果（定理4.1）。此外，我们提供了一些不是局部凸的准点可分离拓扑矢量空间的具体示例。因此，本文的主要定理是Tychonoffs固定点定理在局部凸出拓扑矢量空间上的适当扩展。
In this paper, we introduce the concept of quasi-point-separable topological vector spaces, which has the following important properties: 1.In general, the conditions for a topological vector space to be quasi-point-separable is not very difficult to check; 2.The class of quasi-point-separable topological vector spaces is very large that includes locally convex topological vector spaces and pseudonorm adjoint topological vector spaces as special cases; 3.Every quasi-point-separable Housdorrf topological vector space has the fixed point property (that is, every continuous self-mapping on any given nonempty closed and convex subset has a fixed point), which is the result of the main theorem of this paper (Theorem 4.1). Furthermore, we provide some concrete examples of quasi-point-separable topological vector spaces, which are not locally convex. It follows that the main theorem of this paper is a proper extension of Tychonoffs fixed point theorem on locally convex topological vector spaces.
