Theorems · Definition · global analysis
EuclideanHalfSpace
(n : ℕ) → [NeZero n] → Type
The half-space in ℝ^n, used to model manifolds with boundary. We only define it when
1 ≤ n, as the definition only makes sense in this case.
- Defined in
- Mathlib.Geometry.Manifold.Instances.Real
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- WithLp.ofLpproof · cited by 323
- EuclideanSpaceproof · cited by 307
Cited by51
Results whose statement or proof uses this declaration.
- modelWithCornersEuclideanHalfSpacestatement · cited by 35
- IccLeftChartstatement and proof · cited by 14
- IccRightChartstatement and proof · cited by 11
- contMDiff_subtypeVal_Iccstatement · cited by 4
- contMDiffOn_projIccstatement · cited by 4
- isImmersionOfComplement_subtypeVal_Iccstatement and proof · cited by 3
- frontier_range_modelWithCornersEuclideanHalfSpacestatement · cited by 2
- Icc_chartedSpaceChartAt_of_le_topstatement · cited by 2
- contMDiffOn_comp_projIcc_iffstatement and proof · cited by 2
- Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIccstatement · cited by 2
- Manifold.riemannianEDist_defstatement · cited by 2
- mfderiv_subtypeVal_Icc_onestatement · cited by 1