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Theorems · Theorem · general topology

antilipschitzWith_iff_le_mul_nndist

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {f : α → β},
  AntilipschitzWith K f ↔ ∀ (x y : α), nndist x y ≤ K * nndist (f x) (f y)
Defined in
Mathlib.Topology.MetricSpace.Antilipschitz
Cited by
2 results in Mathlib
Foundations
Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoMetricSpacePseudoMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AntilipschitzWith.of_le_mul_nndist · cited by 1AntilipschitzWith.of_le_m…AntilipschitzWith.le_mul_nndist · cited by 1AntilipschitzWith.le_mul_…NNReal · cited by 4310NNRealPseudoMetricSpace · cited by 1550PseudoMetricSpaceENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealNNDist.nndist · cited by 235NNDist.nndistAntilipschitzWith · cited by 132AntilipschitzWithedist_nndist · cited by 38edist_nndistantilipschitzWith_iff_le_mul_…CITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.