Theorems · Theorem · functional analysis
Balanced.closure
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {A : Set E}
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E], Balanced 𝕜 A → Balanced 𝕜 (closure A)- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normproof · cited by 5,413
- LE.le.transproof · cited by 3,151
- closurestatement · cited by 1,254
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- closure_monoproof · cited by 133
- Balancedstatement and proof · cited by 77
- ContinuousConstSMul.continuous_const_smulproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- AbsConvex.closureproof · cited by 2