Theorems · Theorem · functional analysis
IsCompact.closedBall_mul
∀ {E : Type u_1} [inst : SeminormedCommGroup E] {δ : ℝ} {s : Set E},
IsCompact s → 0 ≤ δ → ∀ (x : E), Metric.closedBall x δ * s = x • Metric.cthickening 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.
Cites10
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
- IsCompactstatement and proof · cited by 1,282
- Metric.closedBallstatement and proof · cited by 704
- Set.smulSetstatement · cited by 608
- Set.mulstatement · cited by 297
- SeminormedCommGroupstatement and proof · cited by 191
- Metric.cthickeningstatement and proof · cited by 113
- IsCompact.mul_closedBallproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsCompact.closedBall_divproof · cited by 0