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Theorems · Theorem · functional analysis

Balanced.zero_mem

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {s : Set E},
  Balanced 𝕜 s → s.Nonempty → 0 ∈ s
Defined in
Mathlib.Analysis.LocallyConvex.BalancedCoreHull
Cited by
1 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingAddCommGroupModule
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Around this declaration

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zero_mem_absConvexHull · cited by 0zero_mem_absConvexHullSet · cited by 53352SetModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupSet.Nonempty · cited by 2627Set.NonemptySeminormedRing · cited by 446SeminormedRingBalanced · cited by 77BalancedbalancedCore_nonempty_iff · cited by 2balancedCore_nonempty_iffBalanced.balancedCore_eq · cited by 1Balanced.balancedCore_eqBalanced.zero_memCITED BYCITES

Cites8

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Cited by1

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