Theorems · Theorem · Lie groups

RestrictedProduct.nhds_eq_map_structureMap

∀ {ι : Type u_1} {R : ι → Type u_2} {A : (i : ι) → Set (R i)} [inst : (i : ι) → TopologicalSpace (R i)],
  (∀ (i : ι), IsOpen (A i)) →
    ∀ (x : (i : ι) → ↑(A i)),
      nhds (RestrictedProduct.structureMap R A Filter.cofinite x) =
        Filter.map (RestrictedProduct.structureMap R A Filter.cofinite) (nhds x)

Defined in

Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace