Theorems · Theorem · general topology
uniformity_basis_edist_nnreal_le
∀ {α : Type u} [inst : PseudoEMetricSpace α], (uniformity α).HasBasis (fun ε => 0 < ε) fun ε => {p | edist p.1 p.2 ≤ ↑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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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredstatement · cited by 6,101
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- le_of_ltproof · cited by 1,175
- uniformitystatement · cited by 765
- EDist.ediststatement · cited by 735
- Filter.HasBasisstatement · cited by 604
- ENNReal.coe_posproof · cited by 37
- ENNReal.lt_iff_exists_nnreal_btwnproof · cited by 17
- EMetric.mk_uniformity_basis_leproof · cited by 3
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