Theorems · Theorem · general topology
Metric.closedEBall_mem_nhds
∀ {α : Type u} [inst : PseudoEMetricSpace α] (x : α) {ε : ENNReal}, 0 < ε → Metric.closedEBall x ε ∈ nhds x- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 146 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 · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.mem_of_supersetproof · cited by 308
- Metric.closedEBallstatement · cited by 107
- Metric.eball_mem_nhdsproof · cited by 25
- Metric.eball_subset_closedEBallproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- continuous_of_le_add_edistproof · cited by 4
- continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWithproof · cited by 3
- Metric.eventually_nhds_zero_forall_closedEBall_subsetproof · cited by 2
- EMetric.closedBall_mem_nhdsproof · cited by 0