Theorems · Theorem · Lie groups

RestrictedProduct.nhds_zero_eq_map_structureMap

∀ {ι : Type u_1} (R : ι → Type u_2) {S : ι → Type u_3} [inst : (i : ι) → SetLike (S i) (R i)] {B : (i : ι) → S i}
  [inst_1 : (i : ι) → TopologicalSpace (R i)] [inst_2 : (i : ι) → Zero (R i)]
  [inst_3 : ∀ (i : ι), ZeroMemClass (S i) (R i)],
  (∀ (i : ι), IsOpen ↑(B i)) →
    nhds (RestrictedProduct.structureMap R (fun i => ↑(B i)) Filter.cofinite 0) =
      Filter.map (RestrictedProduct.structureMap R (fun i => ↑(B i)) Filter.cofinite) (nhds 0)

Defined in

Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SetLikeTopologicalSpaceZeroZeroMemClass