Theorems · Theorem · Lie groups

uniformContinuous_of_continuousAt_zero

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddGroup α] [IsUniformAddGroup α] {hom : Type u_3}
  [inst_3 : UniformSpace β] [inst_4 : AddGroup β] [IsUniformAddGroup β] [inst_6 : FunLike hom α β]
  [AddMonoidHomClass hom α β] (f : hom), ContinuousAt (⇑f) 0 → UniformContinuous ⇑f

An additive group homomorphism (a bundled morphism of a type that implements AddMonoidHomClass) between two uniform additive groups is uniformly continuous provided that it is continuous at zero. See also continuous_of_continuousAt_zero.

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Defs

Cited by

11 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddGroupIsUniformAddGroupUniformSpaceAddGroupIsUniformAddGroupFunLikeAddMonoidHomClass