Theorems · Theorem · functional analysis
Balanced.absorbs_self
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set E}, Balanced 𝕜 s → Absorbs 𝕜 s sA balanced set absorbs itself.
- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NormedDivisionRingstatement and proof · cited by 360
- Balancedstatement and proof · cited by 77
- Absorbsstatement · cited by 59
- Balanced.subset_smulproof · cited by 2
- Absorbs.of_normproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- TotallyBounded.isVonNBoundedproof · cited by 4