Theorems · Theorem · general topology

RestrictedProduct.mapAlongRingHom_apply

∀ {ι₁ : Type u_3} {ι₂ : Type u_4} (R₁ : ι₁ → Type u_5) (R₂ : ι₂ → Type u_6) {𝓕₁ : Filter ι₁} {𝓕₂ : Filter ι₂}
  {S₁ : ι₁ → Type u_7} {S₂ : ι₂ → Type u_8} [inst : (i : ι₁) → SetLike (S₁ i) (R₁ i)]
  [inst_1 : (j : ι₂) → SetLike (S₂ j) (R₂ j)] {B₁ : (i : ι₁) → S₁ i} {B₂ : (j : ι₂) → S₂ j} (f : ι₂ → ι₁)
  (hf : Filter.Tendsto f 𝓕₂ 𝓕₁) [inst_2 : (i : ι₁) → Ring (R₁ i)] [inst_3 : (i : ι₂) → Ring (R₂ i)]
  [inst_4 : ∀ (i : ι₁), SubringClass (S₁ i) (R₁ i)] [inst_5 : ∀ (i : ι₂), SubringClass (S₂ i) (R₂ i)]
  (φ : (j : ι₂) → R₁ (f j) →+* R₂ j) (hφ : ∀ᶠ (j : ι₂) in 𝓕₂, Set.MapsTo ⇑(φ j) ↑(B₁ (f j)) ↑(B₂ j))
  (x : RestrictedProduct (fun i => R₁ i) (fun i => ↑(B₁ i)) 𝓕₁) (j : ι₂),
  ((RestrictedProduct.mapAlongRingHom R₁ R₂ f hf φ hφ) x) j = (φ j) (x (f j))

Defined in

Mathlib.Topology.Algebra.RestrictedProduct.Basic

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

SetLikeSetLikeRingRingSubringClassSubringClass