Theorems · Theorem · sequences and series

Function.LeftInverse.map_tsum

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α]
  {L : SummationFilter β} {G : Type u_4} (f : β → α) [inst_2 : AddCommMonoid γ] [inst_3 : TopologicalSpace γ]
  [T2Space γ] {g : G} [inst_5 : FunLike G α γ] [AddMonoidHomClass G α γ],
  Continuous ⇑g →
    ∀ {g' : γ → α}, Continuous g' → Function.LeftInverse g' ⇑g → g (∑'[L] (b : β), f b) = ∑'[L] (b : β), g (f b)

Special case of Topology.IsClosedEmbedding.map_tsum, logically weaker but possibly easier to apply in practice.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

9 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceAddCommMonoidTopologicalSpaceT2SpaceFunLikeAddMonoidHomClass