Theorems · Theorem · general topology
Metric.ball_zero
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α}, Metric.ball x 0 = ∅- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 115 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- le_reflproof · cited by 2,061
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement · cited by 735
- Metric.ball_eq_emptyproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- gauge_ballproof · cited by 3
- interior_closedBall'proof · cited by 3
- centerMass_mem_ball_of_strictConvexSpaceproof · cited by 1
- MeasureTheory.Measure.addHaar_ball_mulproof · cited by 1
- MeromorphicOn.exists_canonicalDecompproof · cited by 1