Theorems · Theorem · convex and discrete geometry
Set.Nonempty.intrinsicInterior
∀ {V : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [FiniteDimensional ℝ V] {s : Set V},
Convex ℝ s → s.Nonempty → (intrinsicInterior ℝ s).NonemptyThe intrinsic interior of a nonempty convex set is nonempty.
- Defined in
- Mathlib.Analysis.Convex.Intrinsic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topproof · cited by 9,680
- Set.Elemproof · cited by 7,166
- Set.preimageproof · cited by 4,946
- Set.Nonemptystatement and proof · cited by 2,627
- FiniteDimensionalstatement and proof · cited by 1,854
- AffineSubspaceproof · cited by 871
- Convexstatement and proof · cited by 551
- affineSpanproof · cited by 417
Cited by1
Results whose statement or proof uses this declaration.
- intrinsicInterior_nonemptyproof · cited by 1