Theorems · Theorem · general topology
Metric.boundedSpace_iff
∀ {α : Type u} [inst : PseudoMetricSpace α], BoundedSpace α ↔ ∃ C, ∀ (a b : α), dist a b ≤ C- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 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.
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- BoundedSpacestatement · cited by 26
- Metric.isBounded_iffproof · cited by 15
- Bornology.isBounded_univproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- PiNat.boundedSpaceproof · cited by 0