Theorems · Theorem · functional analysis
Seminorm.mem_closedBall_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) {y : E} {r : ℝ}, y ∈ p.closedBall 0 r ↔ p y ≤ r- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- sub_zeroproof · cited by 938
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Seminorm.closedBallstatement · cited by 45
- Seminorm.mem_closedBallproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Seminorm.balanced_closedBall_zeroproof · cited by 1
- Seminorm.closedBall_zero_eqproof · cited by 1
- Seminorm.smul_closedBall_subsetproof · cited by 1
- Seminorm.smul_closedBall_zeroproof · cited by 1
- Seminorm.absorbent_closedBallproof · cited by 0