5 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 \(\FVA\) of finite-valuation approximable domains, a full subcategory of continuous domains contained in the category of pointed countably based FS-domain…
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…
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 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…