Theorems · Theorem · general topology
TopologicalSpace.Compacts.completeSpace_iff
∀ {α : Type u_1} [inst : UniformSpace α], CompleteSpace (TopologicalSpace.Compacts α) ↔ CompleteSpace α- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- TopologicalSpace.Compactsstatement and proof · cited by 386
- IsUniformEmbedding.toIsUniformInducingproof · cited by 44
- Topology.IsClosedEmbedding.isClosed_rangeproof · cited by 41
- IsClosed.isCompleteproof · cited by 19
- TopologicalSpace.NonemptyCompacts.isClosedEmbedding_toCompactsproof · cited by 5
- TopologicalSpace.NonemptyCompacts.isUniformEmbedding_toCompactsproof · cited by 2
- IsUniformInducing.completeSpaceproof · cited by 1
- TopologicalSpace.NonemptyCompacts.completeSpace_iffproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.