Theorems · Theorem · general topology
Metric.nhds_basis_closedBall
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α}, (nhds x).HasBasis (fun ε => 0 < ε) (Metric.closedBall x)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 38 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_leproof · cited by 10
Cited by38
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_one_iffproof · cited by 20
- DifferentiableOn.analyticAtproof · cited by 6
- tendsto_zero_of_isBoundedUnder_smul_of_tendsto_coboundedproof · cited by 5
- BoxIntegral.hasIntegral_iffproof · cited by 5
- VitaliFamily.tendsto_filterAt_iffproof · cited by 5
- Seminorm.continuousAt_zero_of_forall'proof · cited by 4
- SchwartzMap.denseRange_toLpCLMproof · cited by 3
- eventually_closedBall_subsetproof · cited by 3
- Complex.norm_eventually_eq_of_isLocalMaxproof · cited by 2
- BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleOproof · cited by 2
- VitaliFamily.filterAt_basis_closedBallproof · cited by 2
- Euclidean.nhds_basis_closedBallproof · cited by 2