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Theorems · Theorem · general topology

AntilipschitzWith.subsingleton

∀ {α : Type u_4} {β : Type u_5} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  AntilipschitzWith 0 f → Subsingleton α

If f : α → β is 0-antilipschitz, then α is a subsingleton.

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
EMetricSpacePseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AntilipschitzWith.hausdorffMeasure_preimage_le · cited by 2AntilipschitzWith.hausdor…AntilipschitzWith.pos · cited by 0AntilipschitzWith.posNNReal · cited by 4310NNRealMulZeroClass.zero_mul · cited by 1625MulZeroClass.zero_mulPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEDist.edist · cited by 735EDist.edistLE.le.trans_eq · cited by 328le.trans_eqEMetricSpace · cited by 242EMetricSpaceAntilipschitzWith · cited by 132AntilipschitzWithedist_le_zero · cited by 3edist_le_zeroAntilipschitzWith.subsingletonCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.