Theorems · Theorem · general topology

IsUnit.tendsto_const_smul_iff

∀ {M : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Monoid M] [inst_1 : TopologicalSpace α] [inst_2 : MulAction M α]
  [ContinuousConstSMul M α] {f : β → α} {l : Filter β} {a : α} {c : M},
  IsUnit c → (Filter.Tendsto (fun x => c • f x) l (nhds (c • a)) ↔ Filter.Tendsto f l (nhds a))

Defined in

Mathlib.Topology.Algebra.ConstMulAction

Cited by

0 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidTopologicalSpaceMulActionContinuousConstSMul