Theorems · Theorem · general topology
Metric.closedEBall_ofReal
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ},
0 ≤ ε → Metric.closedEBall x (ENNReal.ofReal ε) = Metric.closedBall x εClosed balls defined using the distance or the edistance coincide
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 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.
Cites9
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
- Set.extproof · cited by 2,266
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- ENNReal.ofRealstatement · cited by 863
- Metric.closedBallstatement · cited by 704
- Metric.closedEBallstatement · cited by 107
- edist_le_ofRealproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Metric.closedEBall_coeproof · cited by 4
- Metric.exists_contMDiffMap_forall_closedBall_subsetproof · cited by 0
- Metric.emetric_closedBallproof · cited by 0