Theorems · Theorem · convex and discrete geometry
StrictConvex.linear_image
∀ {𝕜 : Type u_1} {𝕝 : Type u_2} {E : Type u_3} {F : Type u_4} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜]
[inst_2 : TopologicalSpace E] [inst_3 : TopologicalSpace F] [inst_4 : AddCommMonoid E] [inst_5 : AddCommMonoid F]
[inst_6 : Module 𝕜 E] [inst_7 : Module 𝕜 F] {s : Set E} [inst_8 : Semiring 𝕝] [inst_9 : Module 𝕝 E]
[inst_10 : Module 𝕝 F] [LinearMap.CompatibleSMul E F 𝕜 𝕝],
StrictConvex 𝕜 s → ∀ (f : E →ₗ[𝕝] F), IsOpenMap ⇑f → StrictConvex 𝕜 (⇑f '' s)- Defined in
- Mathlib.Analysis.Convex.Strict
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- PartialOrderstatement and proof · cited by 6,410
- Set.imagestatement and proof · cited by 5,609
- map_addproof · cited by 964
- IsOpenMapstatement and proof · cited by 253
Cited by2
Results whose statement or proof uses this declaration.
- StrictConvex.smulproof · cited by 2
- StrictConvex.is_linear_imageproof · cited by 0