Theorems · Theorem · functional analysis
IsCompact.add_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
- 5 results in Mathlib
- Foundations
- Depth 153 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.
Cites16
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Set.extproof · cited by 2,266
- IsCompactstatement and proof · cited by 1,282
- sub_zeroproof · cited by 938
- Metric.closedBallstatement and proof · cited by 704
- Set.addstatement · cited by 338
- Set.mem_iUnionproof · cited by 212
- Metric.cthickeningstatement · cited by 113
- Metric.mem_closedBallproof · cited by 42
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- IsCompact.add_closedBallproof · cited by 3
- IsCompact.sub_closedBall_zeroproof · cited by 0
- IsCompact.closedBall_zero_addproof · cited by 0
- IsCompact.closedBall_zero_subproof · cited by 0