Theorems · Theorem · general topology
LipschitzWith.completion_extension
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : MetricSpace β] [CompleteSpace β] {f : α → β}
{K : NNReal}, LipschitzWith K f → LipschitzWith K (UniformSpace.Completion.extension f)- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- MetricSpacestatement and proof · cited by 1,684
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- NNReal.toRealproof · cited by 1,260
- LipschitzWithstatement and proof · cited by 316
- continuous_id'proof · cited by 295
- UniformSpace.Completionstatement and proof · cited by 192
- Continuous.comp'proof · cited by 184
- Continuous.sndproof · cited by 77
- Continuous.fstproof · cited by 73
Cited by1
Results whose statement or proof uses this declaration.
- LipschitzWith.completion_mapproof · cited by 0