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A Dichotomy for Polish Modules

Frisch, Joshua and Shinko, Forte (2022) A Dichotomy for Polish Modules. Israel Journal of Mathematics . ISSN 0021-2172. doi:10.1007/s11856-022-2411-6. (In Press)

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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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Additional Information:We would like to thank Alexander Kechris, Sławomir Solecki, and Todor Tsankov for several helpful comments and remarks. We would also like to thank the anonymous referee for finding an error in an earlier draft, as well as numerous helpful improvements. The authors were partially supported by NSF Grant DMS-1950475.
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Record Number:CaltechAUTHORS:20230113-708423000.8
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ID Code:118794
Deposited By: Research Services Depository
Deposited On:07 Feb 2023 20:18
Last Modified:07 Feb 2023 20:18

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