On polish groups admitting a compatible complete left-invariant metric

Journal of Symbolic Logic 76 (2):437 - 447 (2011)
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Abstract

We prove that the set of all Polish groups admitting a compatible complete left-invariant metric (called CLI) is coanalytic non-Borel as a subset of a standard Borel space of all Polish groups. As an application of this result, we show that there does not exist a weakly universal CLI group. This, in particular, answers in the negative a question of H.Becker

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10.2178/jsl/1305810757

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