Theorems · Theorem · functional analysis
cthickening_closedBall
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] {δ ε : ℝ},
0 ≤ ε → 0 ≤ δ → ∀ (x : E), Metric.cthickening ε (Metric.closedBall x δ) = Metric.closedBall x (ε + δ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.closedBallstatement and proof · cited by 704
- Metric.cthickeningstatement and proof · cited by 113
- add_nonnegproof · cited by 104
- Metric.cthickening_singletonproof · cited by 4
- cthickening_cthickeningproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- closedBall_add_closedBallproof · cited by 1