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Let X be a closed manifold of dimension 2 or higher or the Hilbert cube. Following Uspenskij one can consider the action of Homeo(X) equipped with the compact-open topology on $\Phi \subset 2^{2^X}$, the space of maximal chains in $2^X$, equipped with the Vietoris topology. We show that if one restricts the action to M ⊂ Φ, the space of maximal chains of continua, then the action is minimal but not transitive. Thus one shows that the action of Homeo(X) on $U_{Homeo\left(X\right)}$, the universal minimal space of Homeo(X), is not transitive (improving...