arXiv subjects

Kaiyun Wang

Publications and source records attributed to Kaiyun Wang.

4 recordsLinked to original sources

arXiv2026

The Kelly--Trotter product conjecture for posets of dimension three

Kelly and Trotter conjectured that dim(P x Q) >= dim P + dim Q - 2 for all finite posets P and Q. We prove the conjecture when dim P = dim Q = 3. This also disproves Trotter's conjecture that, for every 1 <= m <= n, there exist finite posets P and Q with dim P = m, dim Q = n, and dim(P x Q) = n. We further prove that dim(C_k x P) = 4 for every finite poset P with dim P = 3 and every crown C_k with k >= 3. The proof uses the classification of 3-irreducible posets and graphs of critical pairs. For the six infinite noncrown families, we construct explicit non-3-colorable subgraphs. The ten fixed posets are handled by an exhaustive 3-coloring search.

math.CO↗

arXiv2023

The set of maximal points of an $ω$-domain need not be a $G_δ$-set

A topological space has a domain model if it is homeomorphic to the maximal point space $\mbox{Max}(P)$ of a domain $P$. Lawson proved that every Polish space $X$ has an $ω$-domain model $P$ and for such a model $P$, $\mbox{Max}(P)$ is a $G_δ$-set of the Scott space of $P$. Martin (2003) then asked whether it is true that for every $ω$-domain $Q$, $\mbox{Max}(Q)$ is $G_δ$-set of the Scott space of $Q$. In this paper, we give a negative answer to Martin's long standing open problem by constructing a counterexample. The counterexample here actually shows that the answer is no even for $ω$-algebraic domains.

math.GN↗

arXiv2022

Big Ramsey degrees in universal inverse limit structures

We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures,extending Zheng's work for the profinite graph to the setting of Fra\"ıssé classes of finite ordered binary relational structures with the Ramsey property. This work is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. Based on these topological Ramsey spaces and the work of Huber-Geschke-Kojman on inverse limits of finite ordered graphs, we prove that for each such Fra\"ıssé class, its universal inverse limit structure has finite big Ramsey degrees under finite Baire-measurable colorings. For such \Fraisse\ classes satisfying free amalgamation as well as finite ordered tournaments and finite partial orders with a linear extension, we characterize the exact big Ramsey degrees.

math.CO↗

arXiv2020

Nonexistence of k-bounded sobrification

In this paper, we will focus on k-bounded sober spaces and show the existence of a T_0 space X not admitting any k-bounded sobrification. This strengthens a result of Zhao, Lu and Wang, who proved that the canonical k-bounded sobrification does not exist. Our work provides a complete solution to a question of Zhao and Ho, and shows that unlike Sob and BSob,the category KBSob of all k-bounded sober spaces is not a reflective subcategory of the category Top_0 of all T_0 spaces. Furthermore, we introduce the notion of qk-bounded sober spaces and prove that the category KBSob is a full reflective subcategory of the category QKBSob of all qk-bounded sober spaces and continuous mappings preserving existing irreducible suprema.

math.GN↗