Theorems · Theorem · general topology
Metric.eventually_isCompact_closedBall
∀ {α : Type u_2} [inst : PseudoMetricSpace α] [WeaklyLocallyCompactSpace α] (x : α),
∀ᶠ (r : ℝ) in nhds 0, IsCompact (Metric.closedBall x r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- nhdsstatement and proof · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- Filter.univ_mem'proof · cited by 1,672
- PseudoMetricSpacestatement and proof · cited by 1,550
- Filter.mp_memproof · cited by 1,537
- IsCompactstatement and proof · cited by 1,282
- Metric.closedBallstatement and proof · cited by 704
- IsCompact.of_isClosed_subsetproof · cited by 67
- WeaklyLocallyCompactSpacestatement and proof · cited by 35
- WeaklyLocallyCompactSpace.exists_compact_mem_nhdsproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Metric.exists_isCompact_closedBallproof · cited by 2