Theorems · Theorem · general topology
CauchyFilter.inseparable_iff_of_le_nhds
∀ {α : Type u} [inst : UniformSpace α] {f g : CauchyFilter α} {a b : α},
↑f ≤ nhds a → ↑g ≤ nhds b → (Inseparable a b ↔ Inseparable f g)- Defined in
- Mathlib.Topology.UniformSpace.Completion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodproof · cited by 1,750
- uniformityproof · cited by 765
- Filter.Tendsto.compproof · cited by 560
- Inseparablestatement and proof · cited by 160
- Cauchystatement · cited by 115
- Prod.mk.etaproof · cited by 84
- Filter.tendsto_sndproof · cited by 30
- Filter.tendsto_fstproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- CauchyFilter.separated_pureCauchy_injectiveproof · cited by 2
- CauchyFilter.inseparable_lim_iffproof · cited by 1