Theorems · Theorem · general topology
TotallyBounded.isBounded
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α}, TotallyBounded s → Bornology.IsBounded sA totally bounded set is bounded
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 115 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.
Cites12
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.iUnionproof · cited by 2,483
- Set.Finiteproof · cited by 1,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballproof · cited by 735
- zero_lt_oneproof · cited by 598
- Bornology.IsBoundedstatement and proof · cited by 293
- TotallyBoundedstatement and proof · cited by 79
- Bornology.IsBounded.subsetproof · cited by 45
- Metric.isBounded_ballproof · cited by 15
- Metric.totallyBounded_iffproof · cited by 5
- Bornology.isBounded_biUnionproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- IsCompact.isBoundedproof · cited by 29
- Metric.isBounded_Iccproof · cited by 5
- Metric.isBounded_Iooproof · cited by 5
- Metric.isBounded_Icoproof · cited by 0
- Metric.isBounded_Iocproof · cited by 0