A dichotomy for Polish modules

Joshua Frisch; Forte Shinko

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arXiv · 2009.05855

A dichotomy for Polish modules

Joshua Frisch·Forte Shinko

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Abstract

Let $R$ be a ring equipped with a proper norm. We show that under suitable conditions on $R$, there is a natural basis under continuous linear injection for the set of Polish $R$-modules which are not countably generated. When $R$ is a division ring, this basis can be taken to be a singleton.

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BibTeX RIS

Joshua Frisch, Forte Shinko. 2020-09-12. A dichotomy for Polish modules. https://arxiv.org/abs/2009.05855

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