Lim-inf convergence in partially ordered sets ✩
Lim-inf convergence in partially ordered sets ✩
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DOI：
10.1016/j.jmaa.2004.11.028
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发表时间：
2005-09
影响因子：
1.3
通讯作者：
Bin Zhao;Dongsheng Zhao
中科院分区：
文献类型：
--
作者：
Bin Zhao;Dongsheng Zhao
完备格中的lim-inf收敛是Scott为了刻画连续格而引入的。本文引入并研究了偏序集上的lim-inf收敛性。主要结果是：对于偏序集P，极限-inf收敛是拓扑的当且仅当P是连续偏序集。本文还讨论了偏序集上lim-inf收敛的一种较弱形式。
The lim-inf convergence in a complete lattice was introduced by Scott to characterize continuous lattices. Here we introduce and study the lim-inf convergence in a partially ordered set. The main result is that for a poset P the lim-inf convergence is topological if and only if P is a continuous poset. A weaker form of lim-inf convergence in posets is also discussed.