1 citations · 1 across the 12 of their papers we have counts for
14 papers
Chain Continuity and Scott-Closed Interpolation
Yuxu Chen
We prove that every chain-continuous dcpo is continuous and that its way-below relation is the relational square of its chain-below relation, answering a question of Erné. A subalg…
-Unique Dcpos: Intrinsic Characterizations and Counterexamples
Yuxu Chen, Xulong He
A dcpo \(D\) is called \(C_σ\)-unique if for every dcpo \(Q\), \( Γ(D)\cong Γ(Q) \) implies \( D\cong Q, \) where \(Γ(D)\) denotes the lattice of Scott-closed subsets of \(D\). We…
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…
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-…
A note on probabilistic powerdomains, RB-domains, and bc-domains
Yuxu Chen
For a finite nonempty poset \(F\), the normalized probabilistic powerdomain \(\Vone(F)\) is an RB-domain exactly when \(F\) is a finite rooted tree. We extend this classification t…
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…
Cone domains separate FS-domains from RB-domains
Yuxu Chen
Let be a closed, convex, pointed and generating cone in a finite-dimensional real vector space , and let \( D_C=(-C)\cup\{\bot\}\) be the negative cone with a new least elem…
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…
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…
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…