Theorems · Theorem · Lie groups

IsUniformAddGroup.uniformContinuous_iff_isOpen_ker

∀ {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] [DiscreteTopology β] [inst_5 : AddGroup β] [IsUniformAddGroup β] [inst_7 : FunLike hom α β]
  [inst_8 : AddMonoidHomClass hom α β] {f : hom}, UniformContinuous ⇑f ↔ IsOpen ↑(↑f).ker

A homomorphism from a uniform additive group to a discrete uniform additive group is continuous if and only if its kernel is open.

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Defs

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddGroupIsUniformAddGroupUniformSpaceDiscreteTopologyAddGroupIsUniformAddGroupFunLikeAddMonoidHomClass