Theorems · Theorem · functional analysis
AffineSubspace.closed_of_finiteDimensional
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace 𝕜] {P : Type u_1} [inst_4 : MetricSpace P] [inst_5 : NormedAddTorsor E P]
(s : AffineSubspace 𝕜 P) [FiniteDimensional 𝕜 ↥s.direction], IsClosed ↑s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SetLike.coestatement · cited by 8,199
- Submodulestatement · cited by 7,192
- CompleteSpacestatement and proof · cited by 2,532
- FiniteDimensionalstatement and proof · cited by 1,854
- MetricSpacestatement and proof · cited by 1,684
- IsClosedstatement · cited by 1,639
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- AffineSubspace.directionstatement and proof · cited by 339
Cited by2
Results whose statement or proof uses this declaration.
- AffineSubspace.euclideanHausdorffMeasure_eq_lintegralproof · cited by 1
- Convex.addHaar_frontierproof · cited by 1