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20222026
most citedContinuity and core compactness of topological spaces

1 citations · 1 across the 12 of their papers we have counts for

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8 papers · 1 filter

math.GN2026

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…

math.GN2026

-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…

cs.LO2026

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…

math.GN2026

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-…

math.GN2026

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…

math.GN2026

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…

math.GN2026

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…

math.CO2026

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…