Theorems · Theorem · Lie groups

continuous_multiset_prod

∀ {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 : Multiset ι),
  (∀ i ∈ s, Continuous (f i)) → Continuous fun a => (Multiset.map (fun i => f i a) s).prod

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

TopologicalSpaceTopologicalSpaceCommMonoidContinuousMul