Theorems · Theorem · general topology
LipschitzWith.mapsTo_ball
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {f : α → β},
LipschitzWith K f → K ≠ 0 → ∀ (x : α) (r : ℝ), Set.MapsTo f (Metric.ball x r) (Metric.ball (f x) (↑K * r))- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- NNReal.toRealstatement · cited by 1,260
- Metric.ballstatement and proof · cited by 735
- Set.MapsTostatement · cited by 732
- LipschitzWithstatement and proof · cited by 316
- LipschitzWith.dist_lt_mul_of_ltproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Complex.norm_eqOn_closedBall_of_isMaxOnproof · cited by 2