Theorems · Theorem · functional analysis
AbsConvex.closure
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedField 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] [IsTopologicalAddGroup E] [ContinuousSMul 𝕜 E] {s : Set E},
AbsConvex 𝕜 s → AbsConvex 𝕜 (closure s)- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- PartialOrderstatement and proof · cited by 6,410
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- closurestatement · cited by 1,254
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- AbsConvexstatement and proof · cited by 31
- Convex.closureproof · cited by 9
- Balanced.closureproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- closedAbsConvexHull_eq_closure_absConvexHullproof · cited by 1
- nhds_hasBasis_absConvex_closedproof · cited by 0