Theorems · Theorem · general topology
Metric.eventually_nhds_iff_ball
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {p : α → Prop},
(∀ᶠ (y : α) in nhds x, p y) ↔ ∃ ε > 0, ∀ y ∈ Metric.ball x ε, p y- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 10 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.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- nhdsstatement · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement · cited by 735
- Metric.mem_nhds_iffproof · cited by 26
Cited by10
Results whose statement or proof uses this declaration.
- hasFDerivAt_integral_of_dominated_loc_of_lipproof · cited by 4
- hasStrictFDerivAt_of_hasFDerivAt_of_continuousAtproof · cited by 2
- ODE_solution_unique_of_eventuallyproof · cited by 1
- FDerivMeasurableAux.mem_A_of_differentiableproof · cited by 1
- ContinuousLinearMap.opNorm_le_of_nhds_zeroproof · cited by 1
- exists_isMIntegralCurveAt_of_contMDiffAtproof · cited by 1
- isIntegralCurveAt_iff_exists_posproof · cited by 1
- sub_isBigO_norm_rpow_add_one_of_fderivproof · cited by 1
- FDerivMeasurableAux.D_subset_differentiable_setproof · cited by 1
- Complex.IsConservativeOn.eventually_nhds_wedgeIntegral_sub_wedgeIntegralproof · cited by 1