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We extend F{\o}lner's amenability criterion to the realm of generaltopological groups. Building on this, we show that a topological group $G$ isamenable if and only if its left translation action can be approximated in auniform manner by amenable actions on the set $G$. As applications we obtain atopological version of Whyte's geometric solution to the von Neumann problemand provide an affirmative answer to a question posed by Rosendal.

On F{\o}lner sets in topological groups