Theorems · Theorem · functional analysis
ball_mul
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (s : Set E) (x : E),
Metric.ball x δ * s = x • Metric.thickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- mul_commproof · cited by 2,262
- Metric.ballstatement and proof · cited by 735
- Set.smulSetstatement · cited by 608
- Set.mulstatement · cited by 297
- SeminormedCommGroupstatement and proof · cited by 191
- Metric.thickeningstatement and proof · cited by 130
- mul_ballproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ball_divproof · cited by 0