Theorems · Theorem · general topology
UniformSpace.has_seq_basis
∀ (α : Type ua) [inst : UniformSpace α] [(uniformity α).IsCountablyGenerated], ∃ V, (uniformity α).HasAntitoneBasis V ∧ ∀ (n : ℕ), (V n).IsSymm
- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- SetRelstatement and proof · cited by 581
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- SetRel.IsSymmstatement and proof · cited by 93
- Filter.HasAntitoneBasisstatement and proof · cited by 43
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- UniformSpace.hasBasis_symmetricproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- UniformSpace.subset_countable_closure_of_almost_dense_setproof · cited by 4
- UniformSpace.metrizable_uniformityproof · cited by 0