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Uniqueness of directed complete posets based on Scott closed set lattices

Dongsheng Zhao ; Luoshan Xu.

In analogy to a result due to Drake and Thron about topological spaces, this paper studies the dcpos (directed complete posets) which are fully determined, among all dcpos, by their lattices of all Scott-closed subsets (such dcpos will be called $C_{\sigma}$-unique). We introduce the notions of&nbsp;[&hellip;]

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On open well-filtered spaces

Chong Shen ; Xiaoyong Xi ; Xiaoquan Xu ; Dongsheng Zhao.

We introduce and study a new class of $T_0$ spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered space; (2) every core-compact open well-filtered space is sober. As an immediate corollary, we deduce that every&nbsp;[&hellip;]

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