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Theorems · Theorem · functional analysis

Seminorm.closedBall_mono

∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E] {x : E}
  {p : Seminorm 𝕜 E} {r₁ r₂ : ℝ}, r₁ ≤ r₂ → p.closedBall x r₁ ⊆ p.closedBall x r₂
Defined in
Mathlib.Analysis.Seminorm
Cited by
1 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingAddCommGroupSMul
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Around this declaration

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Seminorm.continuousAt_zero' · cited by 3Seminorm.continuousAt_zer…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealAddCommGroup · cited by 12871AddCommGroupLE.le.trans · cited by 3151le.transSeminormedRing · cited by 446SeminormedRingSeminorm · cited by 272SeminormSeminorm.closedBall · cited by 45Seminorm.closedBallSeminorm.closedBall_monoCITED BYCITES

Cites8

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Cited by1

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