T_0拓扑空间的拟连续性与交连续性

Quasicontinuity and meet-continuity of T_0 spaces

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. 其主要结果如下: (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.

Abstract:

By means of convergence, We introduce quasicontinuous sapces and meet-continuous sapces based on directed spaces. The main results we obtain are as follows: (1) A T_0 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 T_0 space is a c-space if and only it is quasicontinuous and meet-continuous.