Theorems · Theorem · general topology
IsUniformInducing.isComplete_range
∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β} [CompleteSpace α],
IsUniformInducing f → IsComplete (Set.range f)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement · cited by 4,705
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- IsUniformInducingstatement and proof · cited by 128
- IsCompletestatement · cited by 68
- completeSpace_iff_isComplete_rangeproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- IsUniformEmbedding.isClosedEmbeddingproof · cited by 7
- OrthogonalFamily.range_linearIsometryproof · cited by 1
- AntilipschitzWith.isComplete_rangeproof · cited by 1
- Metric.Sigma.completeSpaceproof · cited by 0