Theorems · Theorem · convex and discrete geometry
disjoint_interior_extremePoints
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [IsTopologicalAddGroup E]
[ContinuousSMul ℝ E] [Nontrivial E] (S : Set E), Disjoint (interior S) (Set.extremePoints ℝ S)- Defined in
- Mathlib.Analysis.Convex.Strict.Extreme
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- add_zeroproof · cited by 2,707
- Nontrivialstatement and proof · cited by 2,416
- Disjointstatement · cited by 2,201
- nhdsWithinproof · cited by 1,912
- IsTopologicalAddGroupstatement and proof · cited by 1,394
Cited by2
Results whose statement or proof uses this declaration.
- StrictConvex.extremePoints_eq_sdiff_interiorproof · cited by 2
- extremePoints_closedBall_subset_sphereproof · cited by 0