Theorems · Theorem · Lie groups

uniformContinuous_of_continuousAt_one

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : Group α] [IsUniformGroup α] {hom : Type u_3}
  [inst_3 : UniformSpace β] [inst_4 : Group β] [IsUniformGroup β] [inst_6 : FunLike hom α β] [MonoidHomClass hom α β]
  (f : hom), ContinuousAt (⇑f) 1 → UniformContinuous ⇑f

A group homomorphism (a bundled morphism of a type that implements MonoidHomClass) between two uniform groups is uniformly continuous provided that it is continuous at one. See also continuous_of_continuousAt_one.

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Defs

Cited by

3 results in Mathlib

Foundations

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

Assumes

UniformSpaceGroupIsUniformGroupUniformSpaceGroupIsUniformGroupFunLikeMonoidHomClass