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 on$l$-dcpos, based on the generalized scott topology, ischaracterized. in particular, it is shown that every continuous$l$-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.