Theorems · Theorem · general topology
Metric.nhds_basis_closedBall_inv_nat_succ
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α},
(nhds x).HasBasis (fun x => True) fun n => Metric.closedBall x (1 / (↑n + 1))- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- nhdsstatement · cited by 5,554
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- Filter.HasBasisstatement · cited by 604
- nhds_basis_uniformityproof · cited by 21
- Metric.uniformity_basis_dist_le_inv_nat_succproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.