Theorems · Theorem · general topology
Metric.eball_ofReal
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ}, Metric.eball x (ENNReal.ofReal ε) = Metric.ball x εBalls defined using the distance or the edistance coincide
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 147 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.
Cites10
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
- ENNReal.ofRealstatement and proof · cited by 863
- Metric.ballstatement · cited by 735
- Metric.eballstatement · cited by 294
- dist_nonnegproof · cited by 126
- edist_distproof · cited by 39
- ENNReal.ofReal_lt_ofReal_iff_of_nonnegproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Metric.eball_coeproof · cited by 13
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2
- analyticWithinAt_of_singleton_memproof · cited by 0
- Metric.emetric_ballproof · cited by 0