Theorems · Theorem · functional analysis
thickening_closedBall
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] {δ ε : ℝ},
0 < ε → 0 ≤ δ → ∀ (x : E), Metric.thickening ε (Metric.closedBall x δ) = Metric.ball x (ε + δ)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement · cited by 704
- Metric.thickeningstatement and proof · cited by 130
- Metric.thickening_singletonproof · cited by 11
- Metric.cthickening_singletonproof · cited by 4
- thickening_cthickeningproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- ball_add_closedBallproof · cited by 2