Theorems · Theorem · Lie groups

continuousOn_list_prod

∀ {ι : Type u_1} {M : Type u_3} {X : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace M]
  [inst_2 : Monoid M] [ContinuousMul M] {f : ι → X → M} (l : List ι) {t : Set X},
  (∀ i ∈ l, ContinuousOn (f i) t) → ContinuousOn (fun a => (List.map (fun i => f i a) l).prod) t

Defined in

Mathlib.Topology.Algebra.Monoid

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceMonoidContinuousMul