Theorems · Theorem · functional analysis
Seminorm.ball_zero_eq_preimage_ball
∀ {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}, p.ball 0 r = ⇑p ⁻¹' Metric.ball 0 r- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 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.coestatement and proof · cited by 62,936
- Setstatement and proof · 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
- Set.ofPredproof · cited by 6,101
- Set.preimagestatement and proof · cited by 4,946
- Metric.ballstatement and proof · cited by 735
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Seminorm.ballstatement · cited by 78
- Seminorm.ball_zero_eqproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- SeminormFamily.filter_eq_iInfproof · cited by 1