Theorems · Theorem · Lie groups

Filter.Tendsto.mul

∀ {M : Type u_1} [inst : TopologicalSpace M] [inst_1 : Mul M] [ContinuousMul M] {α : Type u_2} {f g : α → M}
  {x : Filter α} {a b : M},
  Filter.Tendsto f x (nhds a) → Filter.Tendsto g x (nhds b) → Filter.Tendsto (fun x => f x * g x) x (nhds (a * b))

Defined in

Mathlib.Topology.Algebra.Monoid.Defs

Cited by

74 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceMulContinuousMul