• Corpus ID: 221655257

# A dichotomy for Polish modules

@article{Frisch2020ADF,
title={A dichotomy for Polish modules},
author={Joshua Frisch and Forte Shinko},
journal={arXiv: Logic},
year={2020}
}
• Published 12 September 2020
• Mathematics
• arXiv: Logic
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.

## References

SHOWING 1-10 OF 21 REFERENCES
Homomorphism reductions on Polish groups
It is shown that there is a homomorphism reducible to L of the countable power of the group of increasing homeomorphisms of the unit interval such that every every Kσ subgroup of G^\omega Gω is homomorphicism reduces to L.
UNIVERSAL SUBGROUPS OF POLISH GROUPS
It is shown that for any locally compact Polish group G, the countable power Gω has a universal Kσ subgroup and a universal compactly generated subgroup.
Universal Abelian topological groups
A topological group is said to be universal in a class of topological groups if and if for every group there is a subgroup of  that is isomorphic to  as a topological group. A group is constructed
A Glimm-Effros dichotomy for Borel equivalence relations
• Mathematics
• 1990
A basic dichotomy concerning the structure of the orbit space of a transformation group has been discovered by Glimm [G12] in the locally compact group action case and extended by Effros [E 1, E2] in
BOREL CHROMATIC NUMBERS
• Mathematics
• 1999
We study in this paper graph coloring problems in the context of descriptive set theory. We consider graphs G=(X, R), where the vertex set X is a standard Borel space (i.e., a complete separable
Characterizing Complete Erdős Space
• Mathematics
Abstract The space now known as complete Erdős space ${{\mathfrak{E}}_{\text{c}}}$ was introduced by Paul Erdős in 1940 as the closed subspace of the Hilbert space ${{\ell }^{2}}$ consisting of all