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Theorems · Theorem · functional analysis

Absorbs.of_norm

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] {A B : Set E},
  (∃ r, ∀ (c : 𝕜), r ≤ ‖c‖ → B ⊆ c • A) → Absorbs 𝕜 A B

Alias of the reverse direction of absorbs_iff_norm.

Defined in
Mathlib.Analysis.LocallyConvex.Basic
Cited by
2 results in Mathlib
Foundations
Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingSMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Seminorm.ball_zero_absorbs_ball_zero · cited by 3Seminorm.ball_zero_absorb…Balanced.absorbs_self · cited by 1Balanced.absorbs_selfSet · cited by 53352SetReal · cited by 25697RealNorm.norm · cited by 5413Norm.normSet.smulSet · cited by 608Set.smulSetSeminormedRing · cited by 446SeminormedRingAbsorbs · cited by 59Absorbsabsorbs_iff_norm · cited by 3absorbs_iff_normAbsorbs.of_normCITED BYCITES

Cites7

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Cited by2

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