Abstract
This article is a slightly modified version of the author’s habilitation thesis, presenting his work on topics related to Polish groups, Baire category methods and metric model theory. Nearly all results presented are not new, though some arguments are. Among new results, we show that, for any countably infinite group Γ, all conjugacy classes in the space of actions of Γ on the Urysohn space are meager; and that the group of bounded isometries of the Urysohn space, endowed with the topology of uniform convergence, is path-connected.
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