Theorems · Theorem · general topology
Metric.uniformity_basis_dist_inv_nat_pos
∀ {α : Type u} [inst : PseudoMetricSpace α],
(uniformity α).HasBasis (fun n => 0 < n) fun n => {p | dist p.1 p.2 < 1 / ↑n}- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.ofPredstatement · cited by 6,101
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- uniformitystatement · cited by 765
- Filter.HasBasisstatement · cited by 604
- zero_lt_oneproof · cited by 598
- div_posproof · cited by 337
- Nat.cast_posproof · cited by 113
- Metric.mk_uniformity_basisproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Metric.nhds_basis_ball_inv_nat_posproof · cited by 0