论文标题
弱遇到$ s_ {z} $ - 连续性和$δ_{z} $ - 连续性
Weakly meet $s_{Z}$-continuity and $δ_{Z}$-continuity
论文作者
论文摘要
基于Xu and Luo在\ cite {qzm}中提出的薄弱满足$ s_ {z {z} $ - 我们进一步证明，如果子集系统$ z $满足某些条件，则poset为$ s_ {z {z {z {z} $ - 如果它是弱的，则只有弱遇到了$ s_ $ s_ z $ - s_ z} $ - 改善Ruan和Xu在\ cite {sz}中给出的相关结果。同时，我们为poset提供了一个特征，即弱遇到$ s_ {z} $ - 连续的，即一个较低的遗传性$ z $ z $ -scott拓扑的poset弱遇到$ s_ {z} $ - 只有当它本地弱地满足$ s_ {z {z {z} $ - 持续的情况下，此外，我们在新类别$ \ mathbf {poset_δ} $上引入了一个单子，并表征其$ eilenberg $ -Moore $ ngebras concretly。
Based on the concept of weakly meet $s_{Z}$-continuouity put forward by Xu and Luo in \cite{qzm}, we further prove that if the subset system $Z$ satisfies certain conditions, a poset is $s_{Z}$-continuous if and only if it is weakly meet $s_{Z}$-continuous and $s_{Z}$-quasicontinuous, which improves a related result given by Ruan and Xu in \cite{sz}. Meanwhile, we provide a characterization for the poset to be weakly meet $s_{Z}$-continuous, that is, a poset with a lower hereditary $Z$-Scott topology is weakly meet $s_{Z}$-continuous if and only if it is locally weakly meet $s_{Z}$-continuous. In addition, we introduce a monad on the new category $\mathbf{POSET_δ}$ and characterize its $Eilenberg$-$Moore$ algebras concretely.
