一致空间的超空间拓扑  

Topologies in hyperspaces of uniform spaces

作　　者：黄书棋 陈君豪 梁海兰 HUANG Shuqi;CHEN Junhao;LIANG Hailan(School of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2024年第6期639-642,共4页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学青年基金资助项目(12101129);福建省自然科学基金资助项目(2019J05033);福建省中青年教师教育科研资助项目(JAT190022)。

摘　　要：讨论一致空间诱导的超空间上的一致结构与Vietoris拓扑的基本性质,证明超空间上Vietoris拓扑和一致拓扑的相容性.通过刻画超空间中具有有限交性质集族的极限性质,给出紧Hausdorff的超空间在Vietoris拓扑下仍为紧Hausdorff空间这一经典结果的新证明.In this paper,we discuss basic properties of uniform structures and Vietoris topologies of hyperspaces which induced by uniform spaces,and prove that the Vietoris topology and uniform topology induced by a uniform space are compatible.Moreover,we characterize the limit of the family of sets with finite intersection property,and give a new proof of the hyperspace induced by a compact Hausdorff space is still compact Hausdorff.

关 键 词：一致空间 超空间 VIETORIS拓扑 

分 类 号：O189[理学—数学]