Theorems · Theorem · general topology
Bornology.IsBounded.subset_closedBall_lt
∀ {α : Type u} {s : Set α} [inst : PseudoMetricSpace α],
Bornology.IsBounded s → ∀ (a : ℝ) (c : α), ∃ r, a < r ∧ s ⊆ Metric.closedBall c r- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 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.
Cites9
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
- Realstatement and proof · cited by 25,697
- LE.le.transproof · cited by 3,151
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballproof · cited by 735
- Metric.closedBallstatement and proof · cited by 704
- Bornology.IsBoundedstatement and proof · cited by 293
- Metric.ball_subset_closedBallproof · cited by 46
- Bornology.IsBounded.subset_ball_ltproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- ZLattice.exists_finsetSum_norm_rpow_le_tsumproof · cited by 2
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1
- eventually_singleton_add_smul_subsetproof · cited by 1