Theorems · Theorem · functional analysis
Seminorm.closedBall_sup
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p q : Seminorm 𝕜 E) (e : E) (r : ℝ), (p ⊔ q).closedBall e r = p.closedBall e r ∩ q.closedBall e r- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredproof · cited by 6,101
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Seminorm.closedBallstatement · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.closedBall_finset_sup'proof · cited by 0