Theorems · Theorem · Lie groups

Filter.HasBasis.uniformity_of_nhds_zero

∀ {α : Type u_1} [inst : UniformSpace α] [inst_1 : AddGroup α] [IsUniformAddGroup α] {ι : Sort u_3} {p : ι → Prop}
  {U : ι → Set α}, (nhds 0).HasBasis p U → (uniformity α).HasBasis p fun i => {x | x.2 - x.1 ∈ U i}

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Defs

Cited by

4 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddGroupIsUniformAddGroup