Theorems · Theorem · general topology
IsCompact.isBounded
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α}, IsCompact s → Bornology.IsBounded sA compact set is bounded
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- IsCompactstatement and proof · cited by 1,282
- Bornology.IsBoundedstatement · cited by 293
- IsCompact.totallyBoundedproof · cited by 12
- TotallyBounded.isBoundedproof · cited by 5
Cited by29
Results whose statement or proof uses this declaration.
- IsCompact.exists_bound_of_continuousOnproof · cited by 8
- Metric.cobounded_le_cocompactproof · cited by 4
- IsCompact.cthickeningproof · cited by 4
- ContinuousOn.integrableOn_of_subset_isCompactproof · cited by 3
- BoxIntegral.integrable_of_continuousOnproof · cited by 3
- exists_contDiff_tsupport_subsetproof · cited by 3
- Metric.isCompact_iff_isClosed_boundedproof · cited by 3
- ZLattice.exists_finsetSum_norm_rpow_le_tsumproof · cited by 2
- ConvexBody.isBoundedproof · cited by 2
- Metric.isBounded_of_compactSpaceproof · cited by 2
- locallyIntegrableOn_mul_sum_Iccproof · cited by 2
- tendsto_measure_cthickening_of_isCompactproof · cited by 1