Theorems · Theorem · functional analysis
IsCompact.closedBall_zero_sub
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] {δ : ℝ} {s : Set E},
IsCompact s → 0 ≤ δ → Metric.closedBall 0 δ - s = Metric.cthickening δ (-s)- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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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
- add_commproof · cited by 1,535
- IsCompactstatement and proof · cited by 1,282
- sub_eq_add_negproof · cited by 1,023
- Metric.closedBallstatement and proof · cited by 704
- Set.negstatement · cited by 168
- Set.substatement · cited by 136
- Metric.cthickeningstatement and proof · cited by 113
- IsCompact.negproof · cited by 8
- IsCompact.add_closedBall_zeroproof · cited by 5
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