Theorems · Theorem · general topology
Metric.ordConnected_setOfPred_closedEBall_subset
∀ {α : Type u} [inst : PseudoEMetricSpace α] (x : α) (s : Set α), {r | Metric.closedEBall x r ⊆ s}.OrdConnected- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Set.Iccproof · cited by 1,702
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.OrdConnectedstatement · cited by 161
- Metric.closedEBallstatement and proof · cited by 107
- Metric.closedEBall_subset_closedEBallproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Metric.exists_forall_closedEBall_subset_aux₂proof · cited by 3
- EMetric.ordConnected_setOf_closedBall_subsetproof · cited by 0
- Metric.ordConnected_setOf_closedEBall_subsetproof · cited by 0