Theorems · Theorem · Lie groups

Filter.Tendsto.smul

∀ {M : Type u_1} {X : Type u_2} {α : Type u_4} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace X]
  [inst_2 : SMul M X] [ContinuousSMul M X] {f : α → M} {g : α → X} {l : Filter α} {c : M} {a : X},
  Filter.Tendsto f l (nhds c) → Filter.Tendsto g l (nhds a) → Filter.Tendsto (fun x => f x • g x) l (nhds (c • a))

Defined in

Mathlib.Topology.Algebra.MulAction

Cited by

22 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSMulContinuousSMul