Theorems · Theorem · functional analysis
Seminorm.balanced_closedBall_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
(p : Seminorm 𝕜 E) (r : ℝ), Balanced 𝕜 (p.closedBall 0 r)Closed seminorm-balls at the origin are balanced.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normproof · cited by 5,413
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- NonnegHomClass.apply_nonnegproof · cited by 79
- Balancedstatement · cited by 77
- Seminorm.closedBallstatement and proof · cited by 45
- mul_le_of_le_one_leftproof · cited by 37
- SeminormClass.map_smul_eq_mulproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- balanced_closedBall_zeroproof · cited by 1