Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $Γ$ and any field $\K$, the space of $Γ$-marked groups $G$ such that the group algebra $\K[G]$ is stably finite is compact.

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