Theorems · Theorem · functional analysis
subset_balancedCore
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s t : Set E}, 0 ∈ t → (∀ (a : 𝕜), ‖a‖ ≤ 1 → a • s ⊆ t) → s ⊆ balancedCore 𝕜 t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement and proof · cited by 5,413
- LT.lt.trans_leproof · cited by 678
- Set.smulSetstatement · cited by 608
- zero_lt_oneproof · cited by 598
- NormedDivisionRingstatement and proof · cited by 360
- norm_pos_iffproof · cited by 168
- norm_invproof · cited by 126
- balancedCorestatement · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- balancedCore_mem_nhds_zeroproof · cited by 4