Theorems · Theorem · general topology
IsUniformEmbedding.discreteUniformity
∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] [DiscreteUniformity β] {f : α → β},
IsUniformEmbedding f → DiscreteUniformity α- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- UniformSpacestatement and proof · cited by 2,040
- Filter.principalproof · cited by 740
- Filter.comapproof · cited by 546
- IsUniformEmbeddingstatement and proof · cited by 107
- Filter.comap_principalproof · cited by 47
- IsUniformEmbedding.toIsUniformInducingproof · cited by 44
- SetRel.idproof · cited by 33
- DiscreteUniformitystatement and proof · cited by 25
- IsUniformInducing.comap_uniformityproof · cited by 22
- IsUniformEmbedding.injectiveproof · cited by 13
- DiscreteUniformity.eq_principal_setRelIdproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.Closeds.discreteUniformity_iffproof · cited by 0
- TopologicalSpace.Compacts.discreteUniformity_iffproof · cited by 0
- TopologicalSpace.NonemptyCompacts.discreteUniformity_iffproof · cited by 0