Theorems · Theorem · general topology
Metric.isBounded_sphere
∀ {α : Type u} {x : α} {r : ℝ} [inst : PseudoMetricSpace α], Bornology.IsBounded (Metric.sphere x r)Spheres are bounded
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 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.
Cites7
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
- Metric.spherestatement · cited by 371
- Bornology.IsBoundedstatement · cited by 293
- Bornology.IsBounded.subsetproof · cited by 45
- Metric.sphere_subset_closedBallproof · cited by 24
- Metric.isBounded_closedBallproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Metric.diam_sphere_eqproof · cited by 2