Theorems · Theorem · Lie groups

continuous_of_continuousAt_one

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G] {M : Type u_1} {hom : Type u_2}
  [inst_3 : MulOneClass M] [inst_4 : TopologicalSpace M] [ContinuousMul M] [inst_6 : FunLike hom G M]
  [MonoidHomClass hom G M] (f : hom), ContinuousAt (⇑f) 1 → Continuous ⇑f

A monoid homomorphism (a bundled morphism of a type that implements MonoidHomClass) from a topological group to a topological monoid is continuous provided that it is continuous at one. See also uniformContinuous_of_continuousAt_one.

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

TopologicalSpaceGroupIsTopologicalGroupMulOneClassTopologicalSpaceContinuousMulFunLikeMonoidHomClass