Theorems · Theorem · functional analysis
StrongDual.polar_nonempty
∀ (𝕜 : Type u_4) [inst : NontriviallyNormedField 𝕜] {E : Type u_5} [inst_1 : AddCommMonoid E]
[inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] (s : Set E), (StrongDual.polar 𝕜 s).Nonempty- Defined in
- Mathlib.Analysis.LocallyConvex.Polar
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.Nonemptystatement · cited by 2,627
- StrongDualstatement · cited by 459
- LinearMap.flipproof · cited by 193
- topDualPairingproof · cited by 24
- StrongDual.polarstatement · cited by 19
- LinearMap.polar_nonemptyproof · cited by 1
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