Theorems · Theorem · functional analysis
Submodule.isTopCompl_iff_isCompl_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},
Submodule.IsTopCompl p q ↔ IsCompl p q ∧ IsClosed ↑p ∧ IsClosed ↑q- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- CompleteSpacestatement and proof · cited by 2,532
- IsClosedstatement and proof · cited by 1,639
- IsComplstatement and proof · cited by 351
- Submodule.IsTopComplstatement and proof · cited by 89
- Subspacestatement and proof · cited by 56
- Submodule.IsTopCompl.isComplproof · cited by 44
- Submodule.IsTopCompl.isClosed'proof · cited by 4
- Submodule.IsTopCompl.isClosedproof · cited by 3
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