Theorems · Definition · convex and discrete geometry
intrinsicFrontier
(𝕜 : Type u_1) →
{V : Type u_2} →
{P : Type u_5} →
[inst : Ring 𝕜] →
[inst_1 : AddCommGroup V] → [Module 𝕜 V] → [TopologicalSpace P] → [AddTorsor V P] → Set P → Set PThe intrinsic frontier of a set is its frontier considered as a set in its affine span.
- Defined in
- Mathlib.Analysis.Convex.Intrinsic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- AddTorsorstatement and proof · cited by 1,657
- frontierproof · cited by 214
Cited by21
Results whose statement or proof uses this declaration.
- intrinsicClosure_sdiff_intrinsicFrontierstatement · cited by 2
- intrinsicClosure_sdiff_intrinsicInteriorstatement · cited by 2
- intrinsicInterior_union_intrinsicFrontierstatement · cited by 1
- ContinuousAffineEquiv.intrinsicFrontier_imagestatement · cited by 1
- closure_sdiff_intrinsicFrontierstatement · cited by 1
- closure_sdiff_intrinsicInteriorstatement · cited by 1
- AffineIsometry.intrinsicFrontier_imagestatement · cited by 1
- intrinsicFrontier_emptystatement · cited by 0
- intrinsicFrontier_singletonstatement · cited by 0
- intrinsicFrontier_subsetstatement · cited by 0
- intrinsicFrontier_subset_frontierstatement · cited by 0
- intrinsicFrontier_subset_intrinsicClosurestatement · cited by 0