Theorems · Theorem · general topology

Filter.Tendsto.const_smul

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

Defined in

Mathlib.Topology.Algebra.ConstMulAction

Cited by

13 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceSMulContinuousConstSMul