Theorems · Definition · general topology

LipschitzWith.toLocallyBoundedMap

{α : Type u} →
  {β : Type v} →
    [inst : PseudoMetricSpace α] →
      [inst_1 : PseudoMetricSpace β] → {K : NNReal} → (f : α → β) → LipschitzWith K f → LocallyBoundedMap α β

A Lipschitz continuous map is a locally bounded map.

Defined in: Mathlib.Topology.MetricSpace.Lipschitz
Cited by: 3 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace PseudoMetricSpace

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Cites5

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

NNRealstatement and proof · cited by 4,310
PseudoMetricSpacestatement and proof · cited by 1,550
LipschitzWithstatement and proof · cited by 316
LocallyBoundedMapstatement · cited by 20
LocallyBoundedMap.ofMapBoundedproof · cited by 2

Cited by3

Results whose statement or proof uses this declaration.

LipschitzWith.isBounded_imageproof · cited by 6
LipschitzWith.comap_cobounded_leproof · cited by 3
LipschitzWith.coe_toLocallyBoundedMapstatement · cited by 0