Theorems · Theorem · general topology
EMetric.nhds_eq
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α}, nhds x = ⨅ ε, ⨅ (_ : ε > 0), Filter.principal (Metric.eball x ε)- 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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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- iInfstatement · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.principalstatement · cited by 740
- Metric.eballstatement · cited by 294
- Filter.HasBasis.eq_biInfproof · cited by 15
- Metric.nhds_basis_eballproof · cited by 10
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