Theorems · Theorem · functional analysis
TotallyBounded.absConvexHull
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} [inst_2 : UniformSpace E]
[IsUniformAddGroup E] [lcs : LocallyConvexSpace ℝ E] [ContinuousSMul ℝ E],
TotallyBounded s → TotallyBounded ((absConvexHull ℝ) s)Alias of the reverse direction of totallyBounded_absConvexHull.
- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 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.
- DFunLike.coestatement · cited by 62,936
- 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
- UniformSpacestatement and proof · cited by 2,040
- ContinuousSMulstatement and proof · cited by 1,016
- ClosureOperatorstatement · cited by 371
- IsUniformAddGroupstatement and proof · cited by 342
- LocallyConvexSpacestatement and proof · cited by 81
- TotallyBoundedstatement · cited by 79
- absConvexHullstatement · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- isCompact_closedAbsConvexHull_of_totallyBoundedproof · cited by 0