Quasicontinuity and meet-continuity of T_0 spaces

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.

Key words:directed space, quasicontinuous space, meet-continuous sapce, c-sapce