Theorems · Theorem · convex and discrete geometry
intrinsicInterior_nonempty
∀ {V : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [FiniteDimensional ℝ V] {s : Set V},
Convex ℝ s → ((intrinsicInterior ℝ s).Nonempty ↔ s.Nonempty)- Defined in
- Mathlib.Analysis.Convex.Intrinsic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.Nonemptystatement · cited by 2,627
- FiniteDimensionalstatement and proof · cited by 1,854
- Convexstatement and proof · cited by 551
- intrinsicInteriorstatement and proof · cited by 22
- Set.Nonempty.intrinsicInteriorproof · cited by 1
- intrinsicInterior_emptyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Real.Convex.dimH_eq_finrank_vectorSpanproof · cited by 1