Theorems · Theorem · functional analysis
Seminorm.ball_eq_emptyset
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
(p : Seminorm 𝕜 E) {x : E} {r : ℝ}, r ≤ 0 → p.ball x r = ∅- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 2 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.
Cites14
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LE.le.transproof · cited by 3,151
- Set.extproof · cited by 2,266
- SeminormedRingstatement and proof · cited by 446
- not_ltproof · cited by 306
- Seminormstatement and proof · cited by 272
- NonnegHomClass.apply_nonnegproof · cited by 79
- Seminorm.ballstatement · cited by 78
Cited by2
Results whose statement or proof uses this declaration.
- Seminorm.ball_smul_ballproof · cited by 1
- Seminorm.ball_norm_mul_subsetproof · cited by 0