Theorems · Theorem · general topology
dense_pi
∀ {ι : Type u_5} {α : ι → Type u_6} [inst : (i : ι) → TopologicalSpace (α i)] {s : (i : ι) → Set (α i)} (I : Set ι),
(∀ i ∈ I, Dense (s i)) → Dense (I.pi s)- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univproof · cited by 3,945
- Set.pistatement · cited by 405
- Densestatement and proof · cited by 359
- Dense.closure_eqproof · cited by 24
- Set.pi_univproof · cited by 14
- closure_pi_setproof · cited by 6
- Set.pi_congrproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- UniqueDiffWithinAt.univ_piproof · cited by 2
- DenseRange.piMapproof · cited by 1