Theorems · Theorem · general topology

Filter.hasBasis_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {ι' : ι → Type u_3} {s : (i : ι) → ι' i → Set (α i)}
  {p : (i : ι) → ι' i → Prop},
  (∀ (i : ι), (f i).HasBasis (p i) (s i)) →
    (Filter.pi f).HasBasis (fun If => If.1.Finite ∧ ∀ i ∈ If.1, p i (If.2 i)) fun If => If.1.pi fun i => s i (If.2 i)

Defined in

Mathlib.Order.Filter.Pi

Cited by

5 results in Mathlib

Foundations

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