Theorems · Theorem · general topology
Metric.mem_closedEBall
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {ε : ENNReal}, y ∈ Metric.closedEBall x ε ↔ edist y x ≤ ε- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 108 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.
Cites5
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
- EDist.ediststatement · cited by 735
- Metric.closedEBallstatement · cited by 107
Cited by7
Results whose statement or proof uses this declaration.
- continuous_of_le_add_edistproof · cited by 4
- Metric.mem_closedEBall'proof · cited by 4
- EMetric.subset_countable_closure_of_almost_dense_setproof · cited by 2
- Metric.mem_closedEBall_selfproof · cited by 2
- Metric.mem_closedEBall_commproof · cited by 1
- Metric.disjoint_closedEBall_of_lt_infEDistproof · cited by 1
- EMetric.mem_closedBallproof · cited by 0