Theorems · Theorem · functional analysis
Seminorm.absorbent_closedBall_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
(p : Seminorm 𝕜 E) {r : ℝ}, 0 < r → Absorbent 𝕜 (p.closedBall 0 r)Closed seminorm-balls at the origin are absorbent.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 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.
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NormedDivisionRingstatement and proof · cited by 360
- Seminormstatement and proof · cited by 272
- Absorbentstatement · cited by 60
- Seminorm.closedBallstatement · cited by 45
- Absorbent.monoproof · cited by 7
- Seminorm.ball_subset_closedBallproof · cited by 5
- Seminorm.absorbent_ball_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.absorbent_closedBallproof · cited by 0