Theorems · Theorem · general topology
Metric.closedEBall_coe
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {ε : NNReal}, Metric.closedEBall x ↑ε = Metric.closedBall x ↑εClosed balls defined using the distance or the edistance coincide
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 118 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 and proof · cited by 53,352
- ENNRealproof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealstatement · cited by 1,260
- Metric.closedBallstatement · cited by 704
- NNReal.coe_nonnegproof · cited by 130
- Metric.closedEBallstatement and proof · cited by 107
- ENNReal.ofReal_coe_nnrealproof · cited by 52
- Metric.closedEBall_ofRealproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- convex_closedEBallproof · cited by 1
- Real.volume_closedEBallproof · cited by 1
- Metric.exists_continuous_nnreal_forall_closedBall_subsetproof · cited by 1
- Metric.emetric_closedBall_nnrealproof · cited by 0