标题： 拟阵交集，无限拟阵的基打包和基覆盖 显示英文标题

标题： Matroid intersection, base packing and base covering for infinite matroids

摘要： 作为无限拟阵理论最近发展的一部分，已经提出了许多关于有限拟阵理论中的标准定理如何扩展到无限情况的猜想。 这些包括基底包装、基底覆盖以及拟阵的交集和并集。 我们证明了这些猜想中的几个是等价的，因此每个猜想都为无限拟阵理论的核心问题提供了不同的视角。 对于有限拟阵，这些等价性为对应这些猜想的有限定理提供了新的且更简单的证明。 这种新的观点还使我们能够扩展并简化一些这些猜想已被证明为真的情况的证明。 显示英文摘要

摘要： As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and matroid intersection and union. We show that several of these conjectures are equivalent, so that each gives a perspective on the same central problem of infinite matroid theory. For finite matroids, these equivalences give new and simpler proofs for the finite theorems corresponding to these conjectures. This new point of view also allows us to extend, and simplify the proofs of, some cases where these conjectures were known to be true.