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Let I be an infinite set, {Gi : i ∈ I} be a family of (topological) groups and G = i∈I Gi be its direct product. For J ⊆ I, pJ : G → j∈J Gj denotes the projection. We say that a subgroup H of G is: (i) uniformly controllable in G provided that for every finite set J ⊆ I there exists a finite set K ⊆ I such that pJ (H) = pJ (H ∩ i∈K Gi); (ii) controllable in… (More)

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