论文标题
Tychonoffs固定点定理扩展到准点可分开的拓扑矢量空间
An Extension of Tychonoffs Fixed Point Theorem to Quasi-point Separable Topological Vector Spaces
论文作者
论文摘要
在本文中，我们介绍了M Quasiconvex，最初是M Quasiconvex的概念，以及在拓扑矢量空间上的广义M Quasiconvex功能。然后，我们将可分离点的拓扑矢量空间（通过拓扑二元空间）扩展到准点可分开的拓扑矢量空间，该拓扑矢量空间由通用的M Quasiconvex功能。我们表明，每个假伴有拓扑媒介矢量空间（包括特殊情况）都可以分离。通过fan-kkm定理，我们证明了准点可分开的拓扑矢量空间上的固定点定理。它是[8]中证明的假伴有拓扑矢量空间上固定点定理的扩展。因此，它是Tychonoffs固定点定理在局部凸拓扑矢量空间上的固定点定理，这是一些示例证明的。
In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the topological dual spaces) to quasi-point separable topological vector spaces by families of generalized m-quasiconvex functionals. We show that every pseudonorm adjoint topological vector space, which includes locally convex topological vector spaces as special cases, is quasi-point separable. By the Fan-KKM theorem, we prove a fixed point theorem on quasi-point separable topological vector spaces. It is an extension of the fixed point theorem on pseudonorm adjoint topological vector spaces proved in [8]. Therefore, it is a properextension of Tychonoffs fixed point theorem on locally convex topological vector spaces, which are demonstrated by some examples.
