Theorems · Theorem · general topology
Metric.closure_closedBall
∀ {α : Type u_2} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ}, closure (Metric.closedBall x ε) = Metric.closedBall x ε- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 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.
Cites7
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
- closurestatement · cited by 1,254
- Metric.closedBallstatement · cited by 704
- IsClosed.closure_eqproof · cited by 139
- Metric.isClosed_closedBallproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- frontier_closedBallproof · cited by 4
- frontier_closedBall'proof · cited by 1
- StrictConvexSpace.sphere_subset_extremePoints_closedBallproof · cited by 0