Theorems · Theorem · functional analysis
LinearMap.polar_isClosed
∀ {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) (s : Set E),
IsClosed (B.polar s)- Defined in
- Mathlib.Analysis.LocallyConvex.Polar
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- 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
- IsClosedstatement and proof · cited by 1,639
- NormedCommRingstatement and proof · cited by 218
- LinearMap.flipstatement and proof · cited by 193
- IsClosed.preimageproof · cited by 138
- Metric.isClosed_closedBallproof · cited by 28
- LinearMap.polarstatement · cited by 23
- isClosed_biInterproof · cited by 16
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