Theorems · Theorem · Lie groups

ContinuousAt.fun_mul

∀ {M : Type u_1} [inst : TopologicalSpace M] [inst_1 : Mul M] [ContinuousMul M] {X : Type u_2}
  [inst_3 : TopologicalSpace X] {f g : X → M} {x : X},
  ContinuousAt f x → ContinuousAt g x → ContinuousAt (fun i => f i * g i) x

Eta-expanded form of ContinuousAt.mul

Defined in

Mathlib.Topology.Algebra.Monoid.Defs

Cited by

4 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMulContinuousMulTopologicalSpace