Theorems · Theorem · general topology
completeSpace_coe_iff_isComplete
∀ {α : Type u} [inst : UniformSpace α] {s : Set α}, CompleteSpace ↑s ↔ IsComplete s- Cited by
- 6 results in Mathlib
- Foundations
- Depth 76 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.
Cites9
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
- Set.Elemstatement · cited by 7,166
- CompleteSpacestatement · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- Subtype.range_coeproof · cited by 98
- IsCompletestatement and proof · cited by 68
- IsUniformEmbedding.isUniformInducingproof · cited by 33
- completeSpace_iff_isComplete_rangeproof · cited by 11
- isUniformEmbedding_subtype_valproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- OrthogonalFamily.isInternal_iffproof · cited by 3
- IsComplete.completeSpace_coeproof · cited by 3
- IsCompactOperator.restrict'proof · cited by 2
- LinearMap.continuous_of_isClosed_graphproof · cited by 1
- Submodule.complete_of_finiteDimensionalproof · cited by 1
- MeasureTheory.isComplete_aestronglyMeasurableproof · cited by 1