Theorems · Theorem · functional analysis
Seminorm.closedBall_eq_metric
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) {x : E} {r : ℝ}, p.closedBall x r = Metric.closedBall x r- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 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.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- Set.extproof · cited by 2,266
- Metric.closedBallstatement · cited by 704
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Seminorm.closedBallstatement and proof · cited by 45
- Seminorm.toAddGroupSeminormstatement · cited by 10
- AddGroupSeminorm.toSeminormedAddCommGroupstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.vadd_closedBallproof · cited by 0