Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals

Tomoki Mihara

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arXiv · 2604.10526

Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals

Tomoki Mihara

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Abstract

Let $k$ be a complete valuation field. We formulate a free Banach $k$-vector space as a Banach $k$-vector space with an orthonormal Schauder basis, and an almost free Banach $k$-vector space as a non-Archimedean analogue of an almost free Abelian group. As non-Archimedean analogues of the classical facts that an almost free Abelian group is free under the assumption of the $\aleph_1$-strong compactness or the weak compactness of the cardinality, we show that an almost free Banach $k$-vector space is free under similar assumptions.

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Tomoki Mihara. 2026-04-12. Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals. https://arxiv.org/abs/2604.10526

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