Mathlib Map

Theorems · Theorem · general topology

LocallyLipschitz.const

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (b : β),
  LocallyLipschitz fun x => b

Constant functions are locally Lipschitz.

Defined in
Mathlib.Topology.EMetricSpace.Lipschitz
Cited by
2 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LocallyLipschitz.max_const · cited by 1LocallyLipschitz.max_constLocallyLipschitz.min_const · cited by 1LocallyLipschitz.min_constPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceLocallyLipschitz · cited by 34LocallyLipschitzLipschitzWith.const · cited by 7LipschitzWith.constLipschitzWith.locallyLipschitz · cited by 6LipschitzWith.locallyLips…LocallyLipschitz.constCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.