Theorems · Theorem · Lie groups

IsTopologicalGroup.uniformCauchySeqOn_iff

∀ {ι : Type u_1} {α : Type u_2} {G : Type u_3} [inst : Group G] [u : UniformSpace G] [inst_1 : IsTopologicalGroup G]
  (F : ι → α → G) (p : Filter ι) (s : Set α),
  IsTopologicalGroup.rightUniformSpace G = u →
    (UniformCauchySeqOn F p s ↔ ∀ u_1 ∈ nhds 1, ∀ᶠ (m : ι × ι) in p ×ˢ p, ∀ a ∈ s, F m.2 a / F m.1 a ∈ u_1)

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Basic

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupUniformSpaceIsTopologicalGroup