Theorems · Theorem · functional analysis
IsOpen.balancedHull
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousConstSMul 𝕜 E] {s : Set E}, IsOpen s → 0 ∈ s → IsOpen (balancedHull 𝕜 s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Set.iUnionproof · cited by 2,483
- IsOpenstatement and proof · cited by 2,400
- le_reflproof · cited by 2,061
- one_smulproof · cited by 1,374
- eq_or_neproof · cited by 1,117
- ContinuousConstSMulstatement and proof · cited by 832
- NormedDivisionRingstatement and proof · cited by 360
Cited by1
Results whose statement or proof uses this declaration.
- IsOpen.absConvexHullproof · cited by 1