Theorems · Theorem · general topology
Metric.nhds_basis_eball
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α}, (nhds x).HasBasis (fun ε => 0 < ε) (Metric.eball x)- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 140 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.
- ENNRealstatement · cited by 9,879
- nhdsstatement · cited by 5,554
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.HasBasisstatement · cited by 604
- Metric.eballstatement · cited by 294
- nhds_basis_uniformityproof · cited by 21
- uniformity_basis_edistproof · cited by 17
Cited by10
Results whose statement or proof uses this declaration.
- EMetric.mem_closure_iffproof · cited by 6
- EMetric.tendsto_nhdsproof · cited by 4
- EMetric.mem_nhds_iffproof · cited by 3
- Metric.nhdsWithin_basis_eballproof · cited by 3
- EMetric.tendsto_nhds_nhdsproof · cited by 2
- tendsto_iff_edist_tendsto_0proof · cited by 2
- EMetric.tendsto_atTopproof · cited by 1
- MeasureTheory.SimpleFunc.tendsto_nearestPtproof · cited by 1
- EMetric.nhds_basis_eballproof · cited by 0
- EMetric.nhds_eqproof · cited by 0