发表机构
University of Puerto Rico（波多黎各大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究拓扑向量空间中子空间的可数交性质，证明可分F-空间满足该性质，而具有不可数Markushevich基的TVS不满足，并构造反例。
AI 中文摘要
一个拓扑向量空间 E 具有子空间的可数交性质，如果每个交为 $0$ 的闭子空间族都包含一个也可交为 $0$ 的可数子族。我们证明每个可分的 F-空间满足此性质，而具有不可数 Markushevich 基的 TVS 则不满足。最后，我们构造一个不满足此性质的可分 TVS。
英文摘要
A topological vector space E has the countable intersection property for subspaces if every family of closed subspaces intersecting to $0$ contains a countable subfamily that also intersects to $0$. We prove that every separable F-space satisfies this property, whereas a TVS with an uncountable Markushevich basis does not. Finally, we construct a separable TVS that fails to satisfy this property.
