Theorems · Theorem · general topology
IsSeqCompact.isComplete
∀ {X : Type u_1} [inst : UniformSpace X] {s : Set X} [(uniformity X).IsCountablyGenerated],
IsSeqCompact s → IsComplete sA sequentially compact set in a uniform space with countably generated uniformity filter is complete.
- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
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
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Filter.atTopproof · cited by 2,405
- le_reflproof · cited by 2,061
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodproof · cited by 1,750
- Set.iInterproof · cited by 1,084
- Filter.NeBotproof · cited by 853
Cited by1
Results whose statement or proof uses this declaration.
- IsSeqCompact.isCompactproof · cited by 1