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Finite-valuation approximable structures: a solution to the Jung--Tix problem of probabilistic powerdomains
Yuxu Chen, Hui Kou, Zhenchao Lyu
We introduce the category of finite-valuation approximable domains, a full subcategory of continuous domains contained in the category of pointed countably based FS-do…
A Natural Fuzzy Order on Fuzzy Numbers
Hui Kou, Mingchun Xie
This paper introduces a natural fuzzy order on fuzzy numbers that extends the natural orders on real numbers and interval numbers. We investigate its completeness properties and sh…
The reflective hull of the two-element chain in DCPO: properness, maximal Γ-faithfulness, and an internal reflection formula
Xulong He, Zhenchao Lyu, Yuxu Chen +1
Let \(\DCPO\) be the category of dcpos and Scott-continuous maps, and let \(\Rtwo\) be the reflective hull of the two-element chain \(2\). We prove that \(\Rtwo\) is the least non-…
FS-domains are not always RB-domains
Yuxu Chen, Hui Kou, Zhenchao Lyu
We prove that Lawson's planar closed-disk domain is not an RB-domain. This domain is the dcpo of all closed disks in the Euclidean plane, together with the whole plane as bottom, o…
Characterizing finite posets whose probabilistic powerdomain are RB-domains
Yuxu Chen, Hui Kou, Zhenchao Lyu
We classify the finite posets whose probabilistic powerdomain is an RB-domain. For a finite nonempty poset \(P\), let \(\Vone(P)\) be the probability powerdomain of , which is t…