Theorems · Theorem · general topology
cauchy_nhds
∀ {α : Type u} [uniformSpace : UniformSpace α] {a : α}, Cauchy (nhds a)- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 78 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- nhdsstatement · cited by 5,554
- UniformSpacestatement and proof · cited by 2,040
- Eq.trans_leproof · cited by 155
- Cauchystatement · cited by 115
- nhds_prod_eqproof · cited by 84
- nhds_le_uniformityproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- isCompact_iff_totallyBounded_isCompleteproof · cited by 6
- IsComplete.isClosedproof · cited by 6
- cauchy_iff_exists_le_nhdsproof · cited by 3
- uniformly_extend_existsproof · cited by 3
- cauchy_pureproof · cited by 2
- UniformSpace.Completion.continuous_hatInvproof · cited by 1
- Filter.Tendsto.cauchy_mapproof · cited by 1