Theorems · Theorem · general topology
TotallyBounded.isCompact_of_isComplete
∀ {α : Type u} [uniformSpace : UniformSpace α] {s : Set α}, TotallyBounded s → IsComplete s → IsCompact s- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 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.
- Setstatement and proof · cited by 53,352
- UniformSpacestatement and proof · cited by 2,040
- IsCompactstatement · cited by 1,282
- TotallyBoundedstatement and proof · cited by 79
- IsCompletestatement and proof · cited by 68
- isCompact_iff_totallyBounded_isCompleteproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- TotallyBounded.isCompact_of_isClosedproof · cited by 5
- isCompact_closure_of_totallyBounded_quasiCompleteproof · cited by 1