Theorems · Theorem · functional analysis
smul_ball
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
{c : 𝕜}, c ≠ 0 → ∀ (x : E) (r : ℝ), c • Metric.ball x r = Metric.ball (c • x) (‖c‖ * r)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Set.extproof · cited by 2,266
- mul_commproof · cited by 2,262
- Dist.distproof · cited by 1,539
- NormedFieldstatement and proof · cited by 1,084
- Metric.ballstatement and proof · cited by 735
- Set.smulSetstatement · cited by 608
- norm_pos_iffproof · cited by 168
Cited by3
Results whose statement or proof uses this declaration.
- smul_closedBall'proof · cited by 3
- MeasureTheory.Measure.addHaar_ball_mul_of_posproof · cited by 2
- smul_unitBallproof · cited by 2