4 citations · 5 across the 12 of their papers we have counts for
13 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…
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…
The Scott space of lattice of closed subsets with supremum operator as a topological semilattice
Yu Chen, Hui Kou, Zhenchao Lyu +1
We present several equivalent conditions of the continuity of the supremum function from the square of the Scott space of to itself under mild assumptions, where deno…
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…
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…
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…
Core-compactness of Smyth powerspaces
Zhenchao Lyu, Xiaodong Jia
We prove that the Smyth powerspace Q(X) of a topological space X is core-compact if and only if X is locally compact. As a straightforward consequence we obtain that the Smyth powe…
Domain-complete and LCS-complete spaces
Matthew de Brecht, Jean Goubault-Larrecq, Xiaodong Jia +1
We study subspaces of continuous dcpos, which we call domain-complete spaces, and subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those in…