Meet-continuity on L-directed Complete Posets

In this paper, the definition of meet-continuity on L-directedcomplete posets (for short, L-dcpos) is introduced. As ageneralization of meet-continuity on crisp dcpos, meet-continuity onL-dcpos, based on the generalized Scott topology, ischaracterized. In particular, it is shown that every continuousL-dcpo is meet-continuous and L-continuous retracts ofmeet-continuous L-dcpos are also meet-continuous. Then, sometopological properties of meet-continuity on L-dcpos arediscussed. It is shown that meet-continuity on L-dcpos is atopological invariant with respect to the generalized Scotttopology, and meet-continuity on L-dcpos is hereditary withrespect to generalized Scott closed subsets.

کلیدواژه ها:

L-dcpo ، Generalized Scott topology ، Meet-continuity