有限拓扑空间中的进一步性
Furtherness in finite topological spaces
AI总结：
本文引入了有限拓扑空间中的一种新的距离-like概念，证明每个有限空间可视为非对称伪度量空间，并提出进一步性矩阵以捕捉空间结构。
摘要：
在本文中，我们为有限拓扑空间引入了一种新的距离-like概念，证明每个有限空间都可以视为非对称伪度量空间。特别地，我们证明每个有限T0空间都是非对称度量空间。由前向球诱导的拓扑与原拓扑一致，而由后向球诱导的拓扑则为相反拓扑。为了捕捉有限空间的必要信息，我们构建了进一步性矩阵，以提供有限空间的显著结构细节。作为应用，我们引入了有限拓扑空间子集的中心和半径概念。
英文摘要：
In this paper, we introduce a novel distance-like notion of furtherness for finite topological spaces, demonstrating that every finite space can be viewed as an asymmetric pseudometric space. In particular, we show that every finite T0 space is asymmetric metric space. The topology induced by the forward balls coincides with the original topology of the space, while the backward balls induce the opposite topology. To capture essential information about each finite space, we construct a furtherness Matrix, which gives significant structural details of the finite space. As an application, we introduce the notion of center and radius of subsets of finite topological spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
