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Theorems · Theorem · general topology

LipschitzWith.of_edist_le

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  (∀ (x y : α), edist (f x) (f y) ≤ edist x y) → LipschitzWith 1 f
Defined in
Mathlib.Topology.EMetricSpace.Lipschitz
Cited by
12 results in Mathlib
Foundations
Depth 148 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.

Isometry.lipschitz · cited by 22Isometry.lipschitzLipschitzWith.id · cited by 8LipschitzWith.idLipschitzWith.prod_fst · cited by 5LipschitzWith.prod_fstLipschitzWith.prod_snd · cited by 5LipschitzWith.prod_sndLipschitzWith.eval · cited by 4LipschitzWith.evalTopologicalSpace.NonemptyCompacts.lipschitz_sup · cited by 1NonemptyCompacts.lipschit…LipschitzWith.subtype_val · cited by 1LipschitzWith.subtype_valTopologicalSpace.NonemptyCompacts.lipschitz_prod · cited by 1NonemptyCompacts.lipschit…TopologicalSpace.Closeds.lipschitz_sup · cited by 1Closeds.lipschitz_supTopologicalSpace.Compacts.lipschitz_prod · cited by 0Compacts.lipschitz_prodTopologicalSpace.Compacts.lipschitz_sup · cited by 0Compacts.lipschitz_supTopologicalSpace.Closeds.lipschitz_prod · cited by 0Closeds.lipschitz_prodENNReal · cited by 9879ENNRealNNReal · cited by 4310NNRealone_mul · cited by 2841one_mulPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEDist.edist · cited by 735EDist.edistLipschitzWith · cited by 316LipschitzWithLipschitzWith.of_edist_leCITED BYCITES

Cites6

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Cited by12

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