T_0拓扑空间的拟连续性与交连续性  

Quasicontinuity and meet-continuity of T_0 spaces

作　　者：冯华容 寇辉[1] 

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）》2017年第5期905-910,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11371262)

摘　　要：本文在定向空间的基础上通过收敛的方式定义了拟连续空间和交连续空间,推广了Domain理论中的相应结果.主要结果如下:(1)一个T_0空间是拟连续的,当且仅当它是局部强紧的,当且仅当它的开集格在集包含关系下是超连续格,当且仅当它的sober化是拟连续dcpo;(2)一个定向空间是交连续的当且仅当它的闭集格在集包含关系下是一个Frame;(3)一个T_0拓扑空间是c-空间当且仅当它既是交连续的又是拟连续的.By means of convergence, we introduce quasicontinuous sapces and meet-continuous sapces based on directed spaces. The main results are as follows. （1） A To space is quascontinuous if and only if it is locally strongly compact, if and only if its open set lattice is a hypercontinuous complete lattice, if and only if it soberfication is a quasicontinuous dcpo; （2） A directed space is meet-continuous iff its closed set lattice is a frame; （3） A To space is a c-space if and only it is quasicontinuous and meet-contin- uous.

关 键 词：定向空间 拟连续性空间 交连续空间 c-空间 

分 类 号：O198.1[理学—数学]