2 results
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 […]
Published on December 18, 2020
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) […]
Published on January 17, 2018