Theorems · Theorem · general topology

Filter.hasBasis_iInf_principal_finite

∀ {α : Type u_1} {ι : Type u_6} (s : ι → Set α),
  (⨅ i, Filter.principal (s i)).HasBasis (fun t => t.Finite) fun t => ⋂ i ∈ t, s i

If s : ι → Set α is an indexed family of sets, then finite intersections of s i form a basis of ⨅ i, 𝓟 (s i).

Defined in

Mathlib.Order.Filter.Bases.Finite

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound