Theorems · Theorem · sequences and series

Function.Injective.hasProd_comap_iff_of_hasSupport

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α]
  {L : SummationFilter β} {f : β → α} {a : α} [L.HasSupport] {g : γ → β} (hg : Function.Injective g),
  (∀ x ∈ L.support, x ∉ Set.range g → f x = 1) →
    (HasProd (f ∘ g) a (L.comap { toFun := g, inj' := hg }) ↔ HasProd f a L)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Defs

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpaceSummationFilter.HasSupport