连续广义度量空间  

Continuous generalized metric spaces

作　　者：余俊澈 YU Jun-Che(College of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2020年第3期417-424,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11871358)。

摘　　要：本文引入并研究了连续广义度量空间.本文首先证明了对于连续的广义度量空间,c-Scott拓扑和广义Scott拓扑相等,然后证明了连续度量空间之间的非扩张映射Yoneda连续当且仅当它关于广义Scott拓扑连续.Continuous generalized metric spaces are introduced and investigated in this paper. It is shown that for such spaces, c-Scott topology is equal to the generalized Scott topology, and that a non-expansive map between such spaces is Yoneda continuous if and only if it is continuous with respect to the generalized Scott topology.

关 键 词：广义度量空间 广义Scott拓扑 c-Scott拓扑 Yoneda连续 

分 类 号：O153.1[理学—数学] O189.11[理学—基础数学]