Theorems · Theorem · Lie groups

continuousOn_finsetProd

∀ {ι : Type u_1} {M : Type u_3} {X : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace M]
  [inst_2 : CommMonoid M] [ContinuousMul M] {f : ι → X → M} (s : Finset ι) {t : Set X},
  (∀ i ∈ s, ContinuousOn (f i) t) → ContinuousOn (fun a => ∏ i ∈ s, f i a) t

Defined in

Mathlib.Topology.Algebra.Monoid

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceCommMonoidContinuousMul