Theorems · Theorem · functional analysis
Submodule.top_orthogonal_eq_bot
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E],
⊤ᗮ = ⊥- Cited by
- 6 results in Mathlib
- Foundations
- Depth 170 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
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
- Submodule.orthogonalstatement and proof · cited by 257
- Submodule.extproof · cited by 204
- Submodule.mem_topproof · cited by 58
- Submodule.mem_botproof · cited by 55
- inner_zero_rightproof · cited by 40
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.orthogonal_eq_bot_iffproof · cited by 7
- Submodule.bot_orthogonal_eq_topproof · cited by 4
- EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_finrank_eq_oneproof · cited by 1
- LinearMap.IsSymmetric.directSum_isInternal_of_pairwise_commuteproof · cited by 1
- Submodule.topologicalClosure_eq_top_iffproof · cited by 1
- ClosedSubmodule.top_orthogonal_eq_botproof · cited by 0