Theorems · Theorem · convex and discrete geometry
ConvexCone.Pointed.of_nonempty_of_isClosed
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : AddCommMonoid E] [inst_1 : TopologicalSpace E] [inst_2 : Semifield 𝕜]
[inst_3 : LinearOrder 𝕜] [inst_4 : Module 𝕜 E] [inst_5 : TopologicalSpace 𝕜] [OrderTopology 𝕜] [DenselyOrdered 𝕜]
[NoMaxOrder 𝕜] [ContinuousSMul 𝕜 E] {C : ConvexCone 𝕜 E}, (↑C).Nonempty → IsClosed ↑C → C.Pointed- Defined in
- Mathlib.Analysis.Convex.Cone.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- IsClosedstatement and proof · cited by 1,639
- Set.Ioiproof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- closureproof · cited by 1,254
- ContinuousSMulstatement and proof · cited by 1,016
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