Theorems · Theorem · general topology
Bornology.IsBounded.subset_ball_lt
∀ {α : Type u} {s : Set α} [inst : PseudoMetricSpace α],
Bornology.IsBounded s → ∀ (a : ℝ) (c : α), ∃ r, a < r ∧ s ⊆ Metric.ball c r- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 110 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.
Cites13
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
- LE.le.trans_ltproof · cited by 795
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallproof · cited by 704
- Bornology.IsBoundedstatement and proof · cited by 293
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- lt_add_oneproof · cited by 105
- Metric.closedBall_subset_ballproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- Bornology.IsBounded.subset_closedBall_ltproof · cited by 3
- Bornology.IsBounded.subset_ballproof · cited by 2
- Bornology.IsBounded.uniformContinuousOn_smulproof · cited by 1
- BoxIntegral.le_hasIntegralVertices_of_isBoundedproof · cited by 1