Weakly meet sZ-continuity and δZ-continuity
Abstract
Based on the concept of weakly meet sZ-continuouity put forward by Xu and Luo in qzm, we further prove that if the subset system Z satisfies certain conditions, a poset is sZ-continuous if and only if it is weakly meet sZ-continuous and sZ-quasicontinuous, which improves a related result given by Ruan and Xu in sz. Meanwhile, we provide a characterization for the poset to be weakly meet sZ-continuous, that is, a poset with a lower hereditary Z-Scott topology is weakly meet sZ-continuous if and only if it is locally weakly meet sZ-continuous. In addition, we introduce a monad on the new category POSETδ and characterize its Eilenberg-Moore algebras concretely.
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