可数S_2-拟连续偏序集上的收敛

Convergence in Countably S_2-quasicontinuous Posets

本文引入了可数S_2-拟连续偏序集、GS*-收敛和弱可数Scott拓扑的概念,给出了可数S_2-拟连续偏序集的收敛刻画:偏序集P是可数S_2-拟连续的当且仅当GS*-收敛关于弱可数Scott拓扑是可拓扑化的。

In this paper, we introduce the concept of the countably S2-quasicontinuous poset GS^＊-convergence and consider the corresponding type of Scott topology - weak countable topology. The main result is a poset is a countably S2-quasicontinuous posets if and only s and scott if the GS^＊-convergence in P is topological with respect to the weak countable Scott topology.