Theorems · Theorem · general topology
UniformSpace.hasBasis_symmetric
∀ {α : Type ua} [inst : UniformSpace α], (uniformity α).HasBasis (fun s => s ∈ uniformity α ∧ s.IsSymm) idSymmetric entourages form a basis of 𝓤 α
- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- Filter.HasBasisstatement · cited by 604
- SetRelstatement · cited by 581
- SetRel.IsSymmstatement · cited by 93
- Filter.hasBasis_selfproof · cited by 17
- SetRel.symmetrizeproof · cited by 15
- symmetrize_mem_uniformityproof · cited by 11
- SetRel.symmetrize_subset_selfproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- UniformSpace.has_seq_basisproof · cited by 2
- eq_of_forall_symmetricproof · cited by 1
- Dynamics.IsDynCoverOf.closureproof · cited by 1
- closure_eq_inter_uniformityproof · cited by 0
- totallyBounded_of_forall_isSymmproof · cited by 0