局部dcpo和相容dcpo的交连续性再讨论

Local Directed Complete Posets and Consistent Directed Complete Posets:Meet-continuity Revisited

在局部dcpo和相容dcpo的交连续性的概念的基础上,对局部dopo和相容dcpo的交连续性作了进一步的探讨,丰富并扩展了有关性质和结论.主要结果是局部dcpo的交连续性定理1和关于相容dcpo交连续性的几个命题.证明了半格(或格)上局部dcpo的交连续性的几个等价条件,且证明了若半格L是交连续的相容dcpo,σ(L)是连续格,则ΛL是Hausdorff空间当且仅当{(x,y)∈L×L:x≤y}是ΛL×ΛL中闭集等.

In this paper, the properties of meet-continuity in local directed complete posets（DC- PO） and consistent directed complete posets are revisited and some relevant conclusions are enriched and developed, basing on the concepts of meet-continuity in local directed complete posets and consistent directed complete posets. The main results are Theorem 1 about the meet-continuity in local directed complete posets and some propositions about meet-continuity in consistent directed complete posets. It proves some equivalent conditions on meet-continuous local directed complete posers and semilattices or lattices, and it proves that in a meet-continuous consistent directed complete posers and a semilattice L with a continuous lattice σ（L）, the consistent Lawson topology AL is Hausdorff if { （x,y）∈L×L：x≤y} is closed in ∧L×∧L.