Theorems · Theorem · general topology
IsUniformEmbedding.toIsUniformInducing
∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
IsUniformEmbedding f → IsUniformInducing f- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsUniformInducingstatement · cited by 128
- IsUniformEmbeddingstatement and proof · cited by 107
Cited by44
Results whose statement or proof uses this declaration.
- IsUniformEmbedding.isUniformInducingproof · cited by 33
- IsUniformEmbedding.isEmbeddingproof · cited by 25
- completeSpace_congrproof · cited by 5
- TopologicalSpace.Closeds.uniformContinuous_coeproof · cited by 5
- TopologicalSpace.NonemptyCompacts.uniformContinuous_coeproof · cited by 4
- TopologicalSpace.Compacts.uniformContinuous_coeproof · cited by 4
- IsUniformEmbedding.discreteUniformityproof · cited by 3
- ArzelaAscoli.isCompact_of_equicontinuousproof · cited by 2
- Filter.HasBasis.compactConvergenceUniformityproof · cited by 2
- ContinuousMap.tendsto_iff_tendstoUniformlyproof · cited by 2
- ContinuousMap.isUniformEmbedding_uniformFunOfFunproof · cited by 2
- TopologicalSpace.Closeds.uniformContinuous_prodproof · cited by 2