Theorems · Theorem · Lie groups

continuous_finprod

∀ {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},
  (∀ (i : ι), Continuous (f i)) →
    (LocallyFinite fun i => Function.mulSupport (f i)) → Continuous fun x => ∏ᶠ (i : ι), f i x

Defined in

Mathlib.Topology.Algebra.Monoid

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceCommMonoidContinuousMul