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引用次数: 0
摘要
本文主要研究正集的 H 闭性和绝对 H 闭性。首先，我们提出了一个反例，指出绝对 H 闭的拓扑半格不一定是 c-完备的，这给出了 Banakh 和 Bardyla 提出的一个开放问题的否定答案。然而，在具有劳森拓扑的连续半格的情况下，我们证明绝对 H 闭拓扑半格意味着 c-完备性。其次，我们利用拓扑嵌入映射获得了准连续网格的特征。最后，在豪斯多夫空间的 H 封闭性和豪斯多夫拓扑半格的绝对 H 封闭性定义的启发下，我们引入了具有劳森拓扑的正集的 H 封闭性和绝对 H 封闭性的概念。
This paper focuses on the study of H-closedness and absolute H-closedness of the posets. First, we propose a counterexample to indicate that an absolutely H-closed topological semilattice may not be c-complete, which gives a negative answer to an open question proposed by Banakh and Bardyla. However, in the case of continuous semilattice with the Lawson topology, we prove that the absolutely H-closed topological semilattice implies c-completeness. Second, we obtain a characterization for quasicontinuous lattices utilizing the topological embedding mapping. Finally, enlightened by the definitions of H-closedness for Hausdorff spaces and absolute H-closedness for Hausdorff topological semilattices, we introduce the concepts of H-closedness and absolute H-closedness for posets with the Lawson topology.
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