It is well-known that a complete lattice L is a meet-continuous lattice if and only ifThis property in fact can be characterized by the Scott topology simply as clσ(↓x ∩ ↓D) = ↓x whenever x ≤ W D. Since the meet operator is not involved, the topological property of meet-continuity can be naturally extended to general dcpos. Such dcpos are also called meet-continuous in this note. It turns out that there exist close relations among meet-continuity, Hausdorff separation, quasicontinuity, continuity and Scott-open filter bases. In particular, we prove that Hausdorff dcpos (via the Lawson topology) need not be quasicontinuous, the category CONT is not a reflective full subcategory of QCONT, the category of quasicontinuous domains, and a dcpo P is meet-continuous when σ(P ) =σ(P ) or it is a semilattice with a T0 T Tσ(D)-topology, whereσ(P ) denote the topology generated by all the Scott-open filters of P . Moreover, under appropriate conditions, the category of dcpos with T0 T Tσ(D)-topology form a cartesian closed category.

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