Theorems · Theorem · functional analysis
smul_unitBall
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
{c : 𝕜}, c ≠ 0 → c • Metric.ball 0 1 = Metric.ball 0 ‖c‖- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- Metric.ballstatement and proof · cited by 735
- smul_zeroproof · cited by 665
- Set.smulSetstatement · cited by 608
- smul_ballproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.w_supportproof · cited by 4
- smul_unitBall_of_posproof · cited by 2