Theorems · Theorem · general topology
Metric.mem_closedEBall_self
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {ε : ENNReal}, x ∈ Metric.closedEBall x ε- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 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.
Cites7
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
- zero_leproof · cited by 382
- Metric.closedEBallstatement · cited by 107
- PseudoEMetricSpace.edist_selfproof · cited by 50
- Metric.mem_closedEBallproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- EMetric.mem_closedBall_selfproof · cited by 0
- Metric.isConnected_closedEBallproof · cited by 0