Theorems · Theorem · Lie groups

Filter.Tendsto.uniformity_add_iff_left

∀ {α : Type u_1} [inst : UniformSpace α] [inst_1 : AddGroup α] [IsUniformAddGroup α] {ι : Type u_3} {f g : ι → α × α}
  {l : Filter ι},
  Filter.Tendsto g l (uniformity α) → (Filter.Tendsto (f + g) l (uniformity α) ↔ Filter.Tendsto f l (uniformity α))

If g : ι → G × G converges to the uniformity, then any f : ι → G × G converges to the uniformity iff f + g does. This is often useful when g is valued in the diagonal, in which case its convergence is automatic.

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Defs

Cited by

0 results in Mathlib

Foundations

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

Assumes

UniformSpaceAddGroupIsUniformAddGroup