1 citations · 1 across the 13 of their papers we have counts for
14 papers
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…
Free dcpo-algebras via directed spaces
Yuxu Chen, Hui Kou, Zhenchao Lyu
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott…
A note on the category of c-spaces
Z. Lyu, X. Xie, H. Kou
We prove that the category of c-spaces with continuous maps is not cartesian closed. As a corollary the category of locally finitary compact spaces with continuous maps is also not…
Free algebras over directed spaces
Yuxu Chen, Hui Kou
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structure…
-convergence and locally hypercompact spaces
Yuxu Chen, Hui Kou
In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of -convergence on a topol…
Monotone determined spaces via -generated spaces
Yuxu Chen, Hui Kou, Zhenchao Lyu
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces gen…
Power structures of directed spaces
Xiaolin Xie, Yuxu Chen, Hui Kou
Powerdomains in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages.\ In this paper,\ we extend the notion of power…
The Directed Probabilistic Powerspace
Xiaolin Xie, Hui Kou, Zhenchao Lyu
Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this…
Continuity and core compactness of topological spaces
Yuxu Chen, Hui Kou, Zhenchao Lyu
We investigate two approximation relations on a T0 topological space, the n-approximation, and the d-approximation, which are generalizations of the way-below relation on a dcpo. D…
Two topologies on the lattice of Scott closed subsets
Yu Chen, Hui Kou, Zhenchao Lyu
For a poset , let and respectively denote the lattice of its Scott open subsets and Scott closed subsets ordered by inclusion, and set . In this paper…