Theorems · Theorem · functional analysis
Seminorm.absorbent_ball
∀ {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} {x : E}, p x < r → Absorbent 𝕜 (p.ball x r)Seminorm-balls containing 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.
Cites16
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
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LE.le.trans_ltproof · cited by 795
- NormedDivisionRingstatement and proof · cited by 360
- Seminormstatement and proof · cited by 272
- sub_posproof · cited by 147
- Seminorm.ballstatement and proof · cited by 78
- Absorbentstatement · cited by 60
- Seminorm.mem_ball_zeroproof · cited by 11
- Seminorm.mem_ballproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- absorbent_ballproof · cited by 1