Theorems · Theorem · functional analysis
convexHull_sphere_eq_closedBall
∀ {F : Type u_2} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] [Nontrivial F] (x : F) {r : ℝ},
0 ≤ r → (convexHull ℝ) (Metric.sphere x r) = Metric.closedBall x r- Defined in
- Mathlib.Analysis.Normed.Module.Convex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites55
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nontrivialstatement and proof · cited by 2,416
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- HVAdd.hVAddproof · cited by 1,820
Cited by1
Results whose statement or proof uses this declaration.
- sphere_subset_range_iff_surjectiveproof · cited by 0