Theorems · Theorem · general topology
Metric.closedBall_subset_cthickening_singleton
∀ {α : Type u_2} [inst : PseudoMetricSpace α] (x : α) (δ : ℝ), Metric.closedBall x δ ⊆ Metric.cthickening δ {x}- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement and proof · cited by 704
- lt_or_geproof · cited by 182
- Metric.cthickeningstatement and proof · cited by 113
- Metric.closedBall_eq_emptyproof · cited by 15
- Metric.cthickening_singletonproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Metric.closedBall_subset_cthickeningproof · cited by 6