Theorems · Theorem · functional analysis
LinearMap.polar_antitone
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedCommRing 𝕜] [inst_1 : AddCommMonoid E]
[inst_2 : AddCommMonoid F] [inst_3 : Module 𝕜 E] [inst_4 : Module 𝕜 F] (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜), Antitone B.polar- Defined in
- Mathlib.Analysis.LocallyConvex.Polar
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 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 · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Antitonestatement · cited by 563
- NormedCommRingstatement and proof · cited by 218
- GaloisConnection.monotone_lproof · cited by 76
- LinearMap.polarstatement · cited by 23
- LinearMap.polar_gcproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- NormedSpace.isBounded_polar_of_mem_nhds_zeroproof · cited by 1
- LinearMap.sInter_polar_finite_subset_eq_polarproof · cited by 1
- NormedSpace.polar_closureproof · cited by 1
- LinearMap.tripolar_eq_polarproof · cited by 0