Theorems · Theorem · convex and discrete geometry
ProperCone.dual_zero
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
[inst_3 : TopologicalSpace R] [inst_4 : ClosedIciTopology R] [inst_5 : AddCommGroup M] [inst_6 : Module R M]
[inst_7 : TopologicalSpace M] [inst_8 : AddCommGroup N] [inst_9 : Module R N] [inst_10 : TopologicalSpace N]
{p : M →ₗ[R] N →ₗ[R] R} [inst_11 : p.IsContPerfPair], ProperCone.dual p 0 = ⊤- Defined in
- Mathlib.Analysis.Convex.Cone.Dual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · 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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Top.topstatement · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- map_zeroproof · cited by 1,614
- IsOrderedRingstatement and proof · cited by 777
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.