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feat(topology/algebra): uniform continuity from 0 (#7318)
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b-mehta committed Apr 23, 2021
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6 changes: 6 additions & 0 deletions src/topology/algebra/uniform_group.lean
Expand Up @@ -132,6 +132,12 @@ begin
exact tendsto.comp h tendsto_comap
end

lemma add_monoid_hom.uniform_continuous_of_continuous_at_zero
[uniform_space β] [add_group β] [uniform_add_group β]
(f : α →+ β) (hf : continuous_at f 0) :
uniform_continuous f :=
uniform_continuous_of_tendsto_zero (by simpa using hf.tendsto)

lemma uniform_continuous_of_continuous [uniform_space β] [add_group β] [uniform_add_group β]
{f : α → β} [is_add_group_hom f] (h : continuous f) :
uniform_continuous f :=
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