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 ${\mathbb K}$ , the space of Γ-marked groups G such that the group algebra ${\mathbb {K}[G]}$ is stably finite is compact.