Theorems · Theorem · general topology
IsUniformInducing.isInducing
∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
IsUniformInducing f → Topology.IsInducing f- Cited by
- 23 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- Topology.IsInducingstatement · cited by 266
- IsUniformInducingstatement and proof · cited by 128
- Topology.IsInducing.inducedproof · cited by 10
- IsUniformInducing.comap_uniformSpaceproof · cited by 4
Cited by23
Results whose statement or proof uses this declaration.
- IsUniformEmbedding.isEmbeddingproof · cited by 25
- IsUniformInducing.isDenseInducingproof · cited by 11
- UniformSpace.Completion.isDenseInducing_coeproof · cited by 11
- AbstractCompletion.isDenseInducingproof · cited by 7
- isComplete_image_iffproof · cited by 5
- Isometry.comp_continuous_iffproof · cited by 5
- IsUniformInducing.isUniformEmbeddingproof · cited by 3
- ArzelaAscoli.isCompact_of_equicontinuousproof · cited by 2
- Isometry.comp_continuousOn_iffproof · cited by 2
- ContinuousMap.tendsto_iff_tendstoUniformlyproof · cited by 2
- ContinuousAlternatingMap.continuous_compContinuousLinearMapCLMproof · cited by 1
- ContinuousMap.continuous_iff_continuous_uniformFunproof · cited by 1