Theorems · Theorem · functional analysis
Seminorm.smul_closedBall_preimage
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
(p : Seminorm 𝕜 E) (y : E) (r : ℝ) (a : 𝕜),
a ≠ 0 → (fun x => a • x) ⁻¹' p.closedBall y r = p.closedBall (a⁻¹ • y) (r / ‖a‖)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
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- Norm.normstatement and proof · cited by 5,413
- Set.preimagestatement · cited by 4,946
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- mul_commproof · cited by 2,262
- NormedDivisionRingstatement and proof · cited by 360
- Seminormstatement and proof · cited by 272
- Set.mem_preimageproof · cited by 190
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