scholarly journals The Solution of Hilbert's Fifth Problem for Transitive Groupoids

2018 ◽  
Author(s):  
Paweł Raźny ◽  
Keyword(s):  
Hilbert’S Fifth Problem

scholarly journals Hilbert’s fifth problem for local groups

2010 ◽  
Vol 172 (2) ◽  
pp. 1269
Author(s):  
Isaac Goldbring
Keyword(s):  
Hilbert’S Fifth Problem

scholarly journals Spatial models of Boolean actions and groups of isometries

2010 ◽  
Vol 31 (2) ◽  
pp. 405-421 ◽  
Author(s):  
ALEKSANDRA KWIATKOWSKA ◽  
SŁAWOMIR SOLECKI
Keyword(s):  
Spatial Model ◽  
Metric Spaces ◽  
Spatial Models ◽  
Locally Compact ◽  
Polish Groups ◽  
Recent Theorem ◽  
Groups Of Isometries ◽  
Hilbert’S Fifth Problem ◽  
Separable Metric Space

AbstractGiven a Polish group G of isometries of a locally compact separable metric space, we prove that each measure-preserving Boolean action by G has a spatial model or, in other words, has a point realization. This result extends both a classical theorem of Mackey and a recent theorem of Glasner and Weiss, and it covers interesting new examples. In order to prove our result, we give a characterization of Polish groups of isometries of locally compact separable metric spaces which may be of independent interest. The solution to Hilbert’s fifth problem plays an important role in establishing this characterization.

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