Theorems · Theorem · convex and discrete geometry
ConvexOn.continuousOn
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {C : Set E} {f : E → ℝ}
[FiniteDimensional ℝ E], IsOpen C → ConvexOn ℝ C f → ContinuousOn f C- Defined in
- Mathlib.Analysis.Convex.Continuous
- 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.
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
- IsOpenstatement and proof · cited by 2,400
- FiniteDimensionalstatement and proof · cited by 1,854
- ContinuousOnstatement · cited by 1,411
- ConvexOnstatement and proof · cited by 232
- LocallyLipschitzOn.continuousOnproof · cited by 6
- ConvexOn.locallyLipschitzOnproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ConvexOn.map_condExp_le_of_finiteDimensionalproof · cited by 1