Theorems · Theorem · functional analysis
Submodule.ClosedComplemented.isClosed
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : TopologicalSpace M] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [ContinuousSub M] [T1Space M] {p : Submodule R M}, p.ClosedComplemented → IsClosed ↑p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsClosedstatement · cited by 1,639
- T1Spacestatement and proof · cited by 275
- ContinuousSubstatement and proof · cited by 48
- Submodule.ClosedComplementedstatement and proof · cited by 40
- Submodule.IsTopCompl.isClosedproof · cited by 3
- Submodule.ClosedComplemented.isTopCompl_complementproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.closedComplemented_iff_isClosed_exists_isClosed_isComplproof · cited by 0