Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Salas, Hector
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214003473
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