Global and local boundedness of Polish groups

Details Global and local boundedness of Polish groups Global and local boundedness of Polish groups

2012-03-27

arxiv.org/abs/1203.6047v1

Mathematics

Functional Analysis

Scientific paper

We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on separable metric spaces). In particular, these properties are characterised by the orbit structure of isometric actions on metric spaces and isometric or continuous affine representations on separable Banach spaces.

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