Theorems · Theorem · general topology
Metric.isBounded_of_compactSpace
∀ {α : Type u} {s : Set α} [inst : PseudoMetricSpace α] [CompactSpace α], Bornology.IsBounded sIn a compact space, all sets are bounded
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- CompactSpacestatement and proof · cited by 593
- Bornology.IsBoundedstatement · cited by 293
- Set.subset_univproof · cited by 228
- isCompact_univproof · cited by 53
- Bornology.IsBounded.subsetproof · cited by 45
- IsCompact.isBoundedproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- GromovHausdorff.HD_candidatesBDist_leproof · cited by 1
- Metric.compactSpace_iff_isBounded_univproof · cited by 1