Theorems · Theorem · general topology
Metric.mem_eball_self
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {ε : ENNReal}, 0 < ε → x ∈ Metric.eball x ε- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.eballstatement · cited by 294
- PseudoEMetricSpace.edist_selfproof · cited by 50
- Metric.mem_eballproof · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- Metric.eball_mem_nhdsproof · cited by 25
- HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sumproof · cited by 2
- Metric.measure_eball_posproof · cited by 2
- Metric.eball_eq_empty_iffproof · cited by 2
- HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpaceproof · cited by 1
- EMetric.mem_ball_selfproof · cited by 0