Theorems · Theorem · general topology
Metric.closedBall_mem_nhds_of_mem
∀ {α : Type u} [inst : PseudoMetricSpace α] {x c : α} {ε : ℝ}, x ∈ Metric.ball c ε → Metric.closedBall c ε ∈ nhds x- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 119 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement · cited by 704
- IsOpen.mem_nhdsproof · cited by 470
- Filter.mem_of_supersetproof · cited by 308
- Metric.isOpen_ballproof · cited by 63
- Metric.ball_subset_closedBallproof · cited by 46
Cited by4
Results whose statement or proof uses this declaration.
- ContDiffBump.eventuallyEq_one_of_mem_ballproof · cited by 1
- Unitary.continuousOn_argSelfAdjointproof · cited by 0