Theorems · Theorem · general topology
Metric.exists_isCompact_closedBall
∀ {α : Type u_2} [inst : PseudoMetricSpace α] [WeaklyLocallyCompactSpace α] (x : α),
∃ r, 0 < r ∧ IsCompact (Metric.closedBall x r)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement and proof · cited by 25,697
- Filter.Eventuallyproof · cited by 3,134
- nhdsWithinproof · cited by 1,912
- PseudoMetricSpacestatement and proof · cited by 1,550
- Set.Ioiproof · cited by 1,463
- IsCompactstatement and proof · cited by 1,282
- Metric.closedBallstatement and proof · cited by 704
- self_mem_nhdsWithinproof · cited by 215
- Filter.Eventually.existsproof · cited by 168
- Filter.Eventually.andproof · cited by 157
- WeaklyLocallyCompactSpacestatement and proof · cited by 35
- eventually_nhdsWithin_of_eventually_nhdsproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- ProperSpace.of_locallyCompactSpaceproof · cited by 6
- ProperSpace.of_nontriviallyNormedField_of_weaklyLocallyCompactSpaceproof · cited by 1