Theorems · Theorem · functional analysis
Seminorm.closedBall_zero_eq
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) {r : ℝ}, p.closedBall 0 r = {y | p y ≤ r}- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredstatement · cited by 6,101
- Set.extproof · cited by 2,266
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Seminorm.closedBallstatement · cited by 45
- Seminorm.mem_closedBall_zeroproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.closedBall_zero_eq_preimage_closedBallproof · cited by 1