  In this paper,the concepts of generalized ideal inf-limit and generalized
ideal final lower bound limit are introduced in the directed complete poset,and
their relations with Scott topology and Lawson topology are studied. The main
results are as follows: (1) On directed complete posets,generalized ideal
inf-limit topology is consistent with Scott topology; (2) Generalized ideal
inf-limiti convergence is topological if and only if directed complete posets
are quasi-continuous domains; (3) In quasi-continuous domain,generalized ideal
final lower bound limit topology is consistent with Lawson topology;(4) In meet
continuous directed complete posets,the generalized ideal final lower bound
limit convergence is topological if and only if the directed complete poset is
continuous.
