Theorems · Theorem · general topology
LipschitzWith.const
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (b : β),
LipschitzWith 0 fun x => bConstant functions are Lipschitz (with any constant).
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- EDist.edistproof · cited by 735
- LipschitzWithstatement · cited by 316
- PseudoEMetricSpace.edist_selfproof · cited by 50
Cited by7
Results whose statement or proof uses this declaration.
- LipschitzWith.max_constproof · cited by 3
- LipschitzOnWith.extend_realproof · cited by 3
- LipschitzWith.ae_lineDifferentiableAtproof · cited by 3
- LocallyLipschitz.constproof · cited by 2
- LipschitzWith.prodMk_leftproof · cited by 1
- LipschitzWith.min_constproof · cited by 1
- LipschitzWith.prodMk_rightproof · cited by 1