Theorems · Theorem · convex and discrete geometry
Real.convex_iff_isPreconnected
∀ {s : Set ℝ}, Convex ℝ s ↔ IsPreconnected s- Defined in
- Mathlib.Analysis.Convex.Topology
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Convexstatement · cited by 551
- IsPreconnectedstatement · cited by 205
- convex_iff_ordConnectedproof · cited by 3
- isPreconnected_iff_ordConnectedproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.convexOn_Gammaproof · cited by 2
- IsPreconnected.convexproof · cited by 0