Theorems · Theorem · functional analysis
IsCompact.sub_closedBall_zero
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] {δ : ℝ} {s : Set E},
IsCompact s → 0 ≤ δ → s - Metric.closedBall 0 δ = Metric.cthickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- IsCompactstatement and proof · cited by 1,282
- sub_eq_add_negproof · cited by 1,023
- Metric.closedBallstatement and proof · cited by 704
- neg_zeroproof · cited by 542
- Set.substatement · cited by 136
- Metric.cthickeningstatement and proof · cited by 113
- neg_closedBallproof · cited by 5
- IsCompact.add_closedBall_zeroproof · cited by 5
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.