Z-quasidistributive and Z-meet-distributive Posets
Z-quasidistributive and Z-meet-distributive Posets
复制标题
Z-拟分配集合和 Z-满足分配集合
DOI：
10.1007/s11083-019-09495-2
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Xu Xiaoquan
中科院分区：
文献类型：
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作者：
Zhang Wenfeng;Xu Xiaoquan
给定偏序集的任意子集选择，本文研究了-预分配性概念的两个弱化，即-拟分配性和-交分配性。前者推广了完备格的拟连续性，后者推广了完备格的交连续性。本文证明了对于全局完备化，拟分配偏序集和交分配偏序集是预分配偏序集。对于-Δ-理想完备化，-拟分配性是-拟分配性加上-拟分配性，条件是幂等元.对于-连续正规完备化：P→N，证明了P的-拟分配性蕴涵N的-拟分配性，且当P是-初始时，其匡威命题也成立。这补充了Erné关于预分配性和交分配性的完备不变性的相应结果。如果是子集系统，且偏序集P的子集上的-below关系具有插值性质，则P是拟分配的，并且可以被一个-连续的映射嵌入到立方体中，且对下拓扑是连续的.
Given any subset selectionfor posets, we study two weakenings of the known concept of-predistributivity, namely,-quasidistributivity and-meet-distributivity. The former generalizes quasicontinuity, and the latter meet-continuity of complete lattices. We show for global completionsthat the-quasidistributive and-meet-distributive posets are the-predistributive ones. For the-Δ-ideal completion,-quasidistributivity is-quasidistributivity plus-quasidistributivity, providedis idempotent. For-continuous normal completionse:P→N, we show that-quasidistributivity ofPimplies that ofN, and the converse holds as well ifeis-initial. This supplements the corresponding results, due to Erné, on the completion-invariance of-predistributivity and-meet-distributivity. Ifis a subset system and the-below relation on the subsets of a posetPhas the interpolation property thenPis-quasidistributive and may be embedded in a cube by a map that is-continuous and continuous for the lower topologies.