Theorems · Theorem · general topology
completeSpace_iff_isComplete_univ
∀ {α : Type u} [uniformSpace : UniformSpace α], CompleteSpace α ↔ IsComplete Set.univ- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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.
- Set.univstatement · cited by 3,945
- CompleteSpacestatement · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- IsCompletestatement · cited by 68
- isComplete_univproof · cited by 5
- completeSpace_of_isComplete_univproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- completeSpace_iff_isComplete_rangeproof · cited by 11
- IsUniformInducing.completeSpace_congrproof · cited by 6
- NormedField.completeSpace_iff_isComplete_closedBallproof · cited by 0