τ-拟连续偏序集的网式刻画

A characterization ofτ-quasicontinuous posets by nets

利用cut算子,在偏序集上引入网的拟下极限收敛概念,讨论了它的一些性质,特别地,对任意包含于σ2-拓扑的序相容拓扑τ,证明了:(1)一个偏序集P是τ-拟连续的当且仅当GS-收敛关于拓扑τ是拓扑的;(2)一个交τ-连续偏序集P是τ-拟连续的当且仅当拟下极限收敛关于拓扑τ∨ω(P)是拓扑的。

In this paper,the concept of quasi-liminf convergence was introduced by means of the cut operator.Some properties of quasi-liminf convergence were investigated.Especially,for any ordered compatible topologyτcontained inσ2-topology,it was proved that:(1)A poset P isτ-quasicontinuous iff the GS-convergence is topological in the topologyτ;(2)A meetτ-continuous poset P is aτ-quasicontinuous poset iff the quasi-liminf convergence is topological in the topologyτ∨ω(P).