Theorems · Theorem · general topology
IsClosed.isComplete
∀ {α : Type u} [uniformSpace : UniformSpace α] [CompleteSpace α] {s : Set α}, IsClosed s → IsComplete s- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceCompleteSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- IsClosedstatement and proof · cited by 1,639
- Filter.principalproof · cited by 740
- Cauchyproof · cited by 115
- le_infproof · cited by 107
- IsCompletestatement · cited by 68
- CompleteSpace.completeproof · cited by 19
- Filter.NeBot.monoproof · cited by 17
Cited by19
Results whose statement or proof uses this declaration.
- TotallyBounded.isCompact_of_isClosedproof · cited by 5
- measurable_derivWithin_Iciproof · cited by 3
- Topology.IsClosedEmbedding.polishSpaceproof · cited by 2
- LinearMap.continuous_of_isClosed_graphproof · cited by 1
- measurable_fderivproof · cited by 1
- measurable_fderiv_with_paramproof · cited by 1
- ContinuousMultilinearMap.completeSpaceproof · cited by 1
- IsDenseInducing.isUniformInducing_extendproof · cited by 1
- isCompact_closure_interUnionBallsproof · cited by 1
- Topology.IsClosedEmbedding.IsCompletelyPseudoMetrizableSpaceproof · cited by 1
- Metric.nonempty_iInter_of_nonempty_biInterproof · cited by 1
- Topology.IsClosedEmbedding.IsCompletelyMetrizableSpaceproof · cited by 1