Theorems · Theorem · functional analysis
ClosedSubmodule.orthogonal_gc
∀ (𝕜 : Type u_4) (E : Type u_5) [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E], GaloisConnection ClosedSubmodule.orthogonal ClosedSubmodule.orthogonal
orthogonal gives a GaloisConnection between
ClosedSubmodule 𝕜 E and its OrderDual.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 181 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- OrderDualstatement and proof · cited by 927
- GaloisConnectionstatement · cited by 253
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmoduleproof · cited by 51
- ClosedSubmodule.orthogonalstatement and proof · cited by 32
- Submodule.inner_left_of_mem_orthogonalproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- ClosedSubmodule.inf_orthogonalproof · cited by 2
- ClosedSubmodule.orthogonal_leproof · cited by 1
- ClosedSubmodule.sInf_orthogonalproof · cited by 0
- ClosedSubmodule.iInf_orthogonalproof · cited by 0