Theorems · Theorem · general topology

isTopologicalBasis_pi

∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] {T : (i : ι) → Set (Set (X i))},
  (∀ (i : ι), TopologicalSpace.IsTopologicalBasis (T i)) →
    TopologicalSpace.IsTopologicalBasis {S | ∃ U F, (∀ i ∈ F, U i ∈ T i) ∧ S = (↑F).pi U}

Defined in

Mathlib.Topology.Bases

Cited by

2 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace