Theorems · Theorem · Lie groups

tendsto_zero_iff_abs_tendsto_zero

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddCommGroup G] [inst_2 : LinearOrder G] [IsOrderedAddMonoid G]
  [OrderTopology G] {α : Type u_2} {l : Filter α} (f : α → G),
  Filter.Tendsto f l (nhds 0) ↔ Filter.Tendsto (abs ∘ f) l (nhds 0)

Defined in

Mathlib.Topology.Algebra.Order.Group

Cited by

4 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupLinearOrderIsOrderedAddMonoidOrderTopology