Theorems · Theorem · general topology
AntilipschitzWith.isClosed_range
∀ {α : Type u_4} {β : Type u_5} [inst : PseudoEMetricSpace α] [inst_1 : EMetricSpace β] [CompleteSpace α] {f : α → β}
{K : NNReal}, AntilipschitzWith K f → UniformContinuous f → IsClosed (Set.range f)- Cited by
- 4 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement · cited by 4,705
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- IsClosedstatement · cited by 1,639
- PseudoEMetricSpacestatement and proof · cited by 1,536
- UniformContinuousstatement and proof · cited by 410
- EMetricSpacestatement and proof · cited by 242
- AntilipschitzWithstatement and proof · cited by 132
- IsComplete.isClosedproof · cited by 6
- AntilipschitzWith.isComplete_rangeproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AntilipschitzWith.isClosedEmbeddingproof · cited by 3
- ContinuousLinearMap.closed_range_of_antilipschitzproof · cited by 1
- ContinuousLinearMap.isClosed_range_iff_antilipschitz_of_injectiveproof · cited by 0
- IsCoercive.isClosed_rangeproof · cited by 0