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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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Domains via approximation operators

Zhiwei Zou ; Qingguo Li ; Weng Kin Ho.

In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal ways to establishing novel domain-theoretic results.&nbsp;[&hellip;]

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Topological Scott Convergence Theorem

Hadrian Andradi ; Weng Kin Ho.

Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the&nbsp;[&hellip;]

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