Theorems · Theorem · functional analysis
Seminorm.closedBall_bot
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {r : ℝ}
(x : E), 0 < r → ⊥.closedBall x r = Set.univ- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Bot.botstatement · cited by 4,720
- Set.univstatement · cited by 3,945
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement · cited by 272
- Seminorm.closedBallstatement · cited by 45
- Seminorm.closedBall_zero'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.closedBall_iSupproof · cited by 1