Theorems · Theorem · general topology
Metric.uniformity_basis_dist_le_inv_nat_succ
∀ {α : Type u} [inst : PseudoMetricSpace α],
(uniformity α).HasBasis (fun x => True) fun n => {p | dist p.1 p.2 ≤ 1 / (↑n + 1)}- 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.
Cites12
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
- 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_add_one_posproof · cited by 18
- exists_nat_one_div_ltproof · cited by 7
- Metric.mk_uniformity_basis_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Metric.nhds_basis_closedBall_inv_nat_succproof · cited by 0