AI 中文总结
本文证明了无限族猜想，证明了在特定条件下两个族的闭包联合等于基集。
AI 中文摘要
我们证明了由纳什 - 威廉姆斯（Nash - Williams）提出的关于无限拟阵的拟阵交猜想：若对于\(k\in\{0,1\}\)，\(M_k=(E,{\mathcal I}_k)\)是具有相同基集\(E\)的拟阵，那么存在\(J^*\in{\mathcal I}_0\cap{\mathcal I}_1\)以及不相交子集\(J_k\subseteq J^*\)（\(k\in\{0,1\}\)），使得\(\text{cl}_{M_0}(J_0)\cup\text{cl}_{M_1}(J_1)=E\)。
英文摘要
We prove the matroid intersection conjecture, due to Nash-Williams \cite{ahaziv}, for infinite matroids: If $M_k = (E, {\mathcal I}_k)$ are matroids for $k \in \{0,1\}$, both having the same base set $E$, then there is $J^* \in {\mathcal I}_0 \cap {\mathcal I}_1$ and disjoint subsets $J_k\subseteq J^*$ for $k\in \{0,1\}$ such that $\text{cl}_{M_0}(J_0) \cup \text{cl}_{M_1}(J_1) = E$.
CommentsDefinition of closure operator is erroneous and invalidates results
