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The Ho-Zhao Problem

Weng Kin Ho ; Jean Goubault-Larrecq ; Achim Jung ; Xiaoyong Xi.

Given a poset $P$, the set, $\Gamma(P)$, of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory $\mathbf{C}$ of $\mathbf{Pos}_d$ (the category of posets and Scott-continuous maps) is said to be $\Gamma$-faithful if for any posets $P$ and $Q$ in $\mathbf{C}$, $\Gamma(P)&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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