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Characterization of posets for liminf convergence being topological
Topology and its Applications ( IF 0.6 ) Pub Date : 2021-02-08 , DOI: 10.1016/j.topol.2021.107615
Ao Shen , Jing Lu , Qingguo Li

It is well known in [3] that the liminf convergence is topological in a domain. We supply an example to illustrate that a dcpo in which the liminf convergence is topological may not be continuous in this paper. Naturally, there is a problem raised as follows: in what posets is the liminf convergence topological? First, we show that if the liminf convergence is topological in a poset, then the poset is exact. Second, we prove that a poset L is continuous if and only if L is meet continuous and the liminf convergence is topological in L and the Lawson topology equals the liminf topology. Finally, we introduce the concept of weak* continuous and obtain the result that the liminf convergence is topological in a poset L if and only if L is weak* continuous. This result answers the above problem.



中文翻译:

Liminf收敛的坐姿的特征是拓扑

在[3]中众所周知,线性收敛是域内的拓扑。我们提供了一个示例来说明线性收敛收敛的dcpo在本文中可能不是连续的。自然地,存在一个问题,如下所示:liminf收敛在什么姿势中?首先,我们证明,如果在一个波姿集中线的收敛是拓扑的,那么波姿是精确的。其次,我们证明了一个序集大号是连续的当且仅当大号是满足连续和liminf收敛拓扑中大号和Lawson拓扑等于liminf拓扑。最后,我们引入弱*连续的概念,得到的结果是,liminf融合是一个偏序集拓扑大号当且仅当L是弱*连续的。该结果回答了上述问题。

更新日期:2021-02-11
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