Theorems · Theorem · general topology
EMetric.nhds_basis_eball
Deprecated since 2026-01-24Use Metric.nhds_basis_eball instead.
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α}, (nhds x).HasBasis (fun ε => 0 < ε) (Metric.eball x)Alias of Metric.nhds_basis_eball.
- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites6
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 · cited by 1,536
- Filter.HasBasisstatement · cited by 604
- Metric.eballstatement · cited by 294
- Metric.nhds_basis_eballproof · cited by 10
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