Theorems · Theorem · general topology
UniformSpace.metrizable_uniformity
∀ (X : Type u_2) [inst : UniformSpace X] [(uniformity X).IsCountablyGenerated], ∃ I, PseudoMetricSpace.toUniformSpace = inst
If X is a uniform space with countably generated uniformity filter, there exists a
PseudoMetricSpace structure compatible with the UniformSpace structure. Use
UniformSpace.pseudoMetricSpace or UniformSpace.metricSpace instead.
- Defined in
- Mathlib.Topology.Metrizable.Uniformity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites68
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- NNRealproof · cited by 4,310
- UniformSpacestatement and proof · cited by 2,040
- le_rflproof · cited by 1,558
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- NNReal.toRealproof · cited by 1,260
- Set.Iooproof · cited by 1,214
- le_transproof · cited by 985
- one_ne_zeroproof · cited by 885
- LE.le.trans_ltproof · cited by 795
Cited by1
Results whose statement or proof uses this declaration.
- UniformSpace.pseudoMetricSpaceproof · cited by 0