Theorems · Theorem · functional analysis
IsCompact.add_closedBall
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] {δ : ℝ} {s : Set E},
IsCompact s → 0 ≤ δ → ∀ (x : E), s + Metric.closedBall x δ = x +ᵥ Metric.cthickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 163 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.
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HVAdd.hVAddstatement and proof · cited by 1,820
- IsCompactstatement and proof · cited by 1,282
- Metric.closedBallstatement and proof · cited by 704
- Set.vaddSetstatement · cited by 403
- Set.addstatement · cited by 338
- Metric.cthickeningstatement and proof · cited by 113
- add_vadd_commproof · cited by 6
- IsCompact.add_closedBall_zeroproof · cited by 5
- vadd_closedBall_zeroproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- closedBall_add_closedBallproof · cited by 1
- IsCompact.closedBall_addproof · cited by 1
- IsCompact.sub_closedBallproof · cited by 0