Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.completeSpace_iff
∀ {α : Type u_1} [inst : UniformSpace α], CompleteSpace (TopologicalSpace.NonemptyCompacts α) ↔ CompleteSpace α- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Filterproof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.Nonemptyproof · cited by 2,627
- CompleteSpacestatement and proof · cited by 2,532
- IsOpenproof · cited by 2,400
- UniformSpacestatement and proof · cited by 2,040
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Filter.mapproof · cited by 819
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.completeSpace_iffproof · cited by 0