Theorems · Theorem · general topology
Set.separatesPoints_lipschitzWith_one
∀ (E : Type u_1) [inst : MetricSpace E], {f | LipschitzWith 1 f}.SeparatesPointsThe set of functions which are 1-Lipschitz on a metric space separates points.
- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.ofPredstatement · cited by 6,101
- NNRealstatement · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- LipschitzWithstatement · cited by 316
- dist_selfproof · cited by 116
- Set.SeparatesPointsstatement · cited by 4
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