Theorems · Theorem · convex and discrete geometry
AmpleSet.vadd
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousAdd E]
{s : Set E}, AmpleSet s → ∀ {y : E}, AmpleSet (y +ᵥ s)Affine translations of ample sets are ample.
- Defined in
- Mathlib.Analysis.Convex.AmpleSet
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- HVAdd.hVAddstatement · cited by 1,820
- ContinuousAddstatement and proof · cited by 777
- Set.vaddSetstatement · cited by 403
- AmpleSetstatement and proof · cited by 10
- AmpleSet.imageproof · cited by 4
- ContinuousAffineEquiv.constVAddproof · cited by 3
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