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On Polish groups admitting a compatible complete left-invariant metric

Published online by Cambridge University Press:  12 March 2014

Maciej Malicki
Maciej Malicki*
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956, Warsaw, Poland, E-mail: mamalicki@gmail.com
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 437 - 447
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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