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Theorems · Theorem · functional analysis

Balanced.subset_balancedCore_of_subset

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] {s t : Set E},
  Balanced 𝕜 s → s ⊆ t → s ⊆ balancedCore 𝕜 t

The balanced core of t is maximal in the sense that it contains any balanced subset s of t.

Defined in
Mathlib.Analysis.LocallyConvex.BalancedCoreHull
Cited by
2 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingSMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

balancedCore_eq_iInter · cited by 2balancedCore_eq_iInterBalanced.balancedCore_eq · cited by 1Balanced.balancedCore_eqSet · cited by 53352SetSeminormedRing · cited by 446SeminormedRingBalanced · cited by 77BalancedSet.subset_sUnion_of_mem · cited by 39Set.subset_sUnion_of_membalancedCore · cited by 18balancedCoreBalanced.subset_balancedCore_…CITED BYCITES

Cites5

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Cited by2

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