Theorems · Theorem · functional analysis
IsCompact.div_closedBall
∀ {E : Type u_1} [inst : SeminormedCommGroup E] {δ : ℝ} {s : Set E},
IsCompact s → 0 ≤ δ → ∀ (x : E), s / Metric.closedBall x δ = x⁻¹ • Metric.cthickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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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
- IsCompactstatement and proof · cited by 1,282
- div_eq_mul_invproof · cited by 715
- Metric.closedBallstatement and proof · cited by 704
- Set.smulSetstatement · cited by 608
- SeminormedCommGroupstatement and proof · cited by 191
- Metric.cthickeningstatement and proof · cited by 113
- Set.divstatement · cited by 112
- inv_closedBallproof · cited by 3
- IsCompact.mul_closedBallproof · cited by 2
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