Theorems · Theorem · functional analysis
IsCompact.mul_closedBall_one
∀ {E : Type u_1} [inst : SeminormedCommGroup E] {δ : ℝ} {s : Set E},
IsCompact s → 0 ≤ δ → s * Metric.closedBall 1 δ = Metric.cthickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 153 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.
Cites12
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
- Norm.normproof · cited by 5,413
- Set.extproof · cited by 2,266
- IsCompactstatement and proof · cited by 1,282
- Metric.closedBallstatement and proof · cited by 704
- div_oneproof · cited by 629
- Set.mulstatement · cited by 297
- SeminormedCommGroupstatement and proof · cited by 191
- Metric.cthickeningstatement · cited by 113
- dist_eq_norm_divproof · cited by 12
- IsCompact.cthickening_eq_biUnion_closedBallproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsCompact.mul_closedBallproof · cited by 2
- IsCompact.closedBall_one_mulproof · cited by 0
- IsCompact.div_closedBall_oneproof · cited by 0
- IsCompact.closedBall_one_divproof · cited by 0