Theorems · Theorem · functional analysis
Submodule.IsCompl.isTopCompl_of_isClosed
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace E] {p q : Subspace 𝕜 E},
IsCompl p q → IsClosed ↑p → IsClosed ↑q → Submodule.IsTopCompl p q- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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 and proof · cited by 8,199
- Set.Elemproof · cited by 7,166
- CompleteSpacestatement and proof · cited by 2,532
- IsClosedstatement and proof · cited by 1,639
- IsComplstatement and proof · cited by 351
- Submodule.IsTopComplstatement · cited by 89
- Subspacestatement and proof · cited by 56
- Submodule.prodEquivOfIsComplproof · cited by 35
- Submodule.IsCompl.isTopCompl_iff_continuous_symm_prodEquivOfIsComplproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.ClosedComplemented.of_isCompl_isClosedproof · cited by 2
- Submodule.isTopCompl_iff_isCompl_isClosedproof · cited by 0