Theorems · Theorem · general topology
CauchyFilter.separated_pureCauchy_injective
∀ {α : Type u_1} [inst : UniformSpace α] [T0Space α],
Function.Injective fun a => SeparationQuotient.mk (CauchyFilter.pureCauchy a)- Defined in
- Mathlib.Topology.UniformSpace.Completion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceT0Space
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.
- UniformSpacestatement and proof · cited by 2,040
- T0Spacestatement and proof · cited by 179
- SeparationQuotientstatement · cited by 128
- SeparationQuotient.mkstatement and proof · cited by 94
- pure_le_nhdsproof · cited by 39
- CauchyFilterstatement · cited by 19
- Inseparable.eqproof · cited by 19
- CauchyFilter.pureCauchystatement and proof · cited by 9
- SeparationQuotient.mk_eq_mkproof · cited by 7
- CauchyFilter.inseparable_iff_of_le_nhdsproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.isUniformEmbedding_coeproof · cited by 3
- UniformSpace.Completion.isDenseEmbedding_coeproof · cited by 1