Theorems · Theorem · general topology
Metric.sphere_zero
∀ {γ : Type w} [inst : MetricSpace γ] {x : γ}, Metric.sphere x 0 = {x}- Defined in
- Mathlib.Topology.MetricSpace.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
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
- Set.extproof · cited by 2,266
- MetricSpacestatement and proof · cited by 1,684
- Metric.spherestatement · cited by 371
- dist_eq_zeroproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- isPathConnected_sphereproof · cited by 1
- threeAPFree_sphereproof · cited by 1
- smul_sphereproof · cited by 1
- AffineIndependent.existsUnique_dist_eqproof · cited by 1
- MeasureTheory.Measure.addHaar_sphereproof · cited by 0