Theorems · Theorem · Lie groups

continuous_of_continuousAt_zero

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {M : Type u_1}
  {hom : Type u_2} [inst_3 : AddZeroClass M] [inst_4 : TopologicalSpace M] [ContinuousAdd M] [inst_6 : FunLike hom G M]
  [AddMonoidHomClass hom G M] (f : hom), ContinuousAt (⇑f) 0 → Continuous ⇑f

An additive monoid homomorphism (a bundled morphism of a type that implements AddMonoidHomClass) from an additive topological group to an additive topological monoid is continuous provided that it is continuous at zero. See also uniformContinuous_of_continuousAt_zero.

Defined in

Mathlib.Topology.Algebra.Group.Basic

Cited by

5 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddGroupIsTopologicalAddGroupAddZeroClassTopologicalSpaceContinuousAddFunLikeAddMonoidHomClass