Residual finiteness of groups and topological dynamics
Sbornik. Mathematics, Tome 191 (2000) no. 4, pp. 529-541

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The property of residual finiteness of finitely generated groups admits an interpretation in terms of topological dynamics. In this paper it is proved that a finitely generated group is residually finite if and only if it is isomorphic to a group whose action on some compact set is efficient and distal.
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A. V. Egorov. Residual finiteness of groups and topological dynamics. Sbornik. Mathematics, Tome 191 (2000) no. 4, pp. 529-541. http://geodesic.mathdoc.fr/item/SM_2000_191_4_a2/