Theorems · Theorem · functional analysis
Submodule.IsTopCompl.isCompl
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : TopologicalSpace M] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] {p q : Submodule R M}, Submodule.IsTopCompl p q → IsCompl p q- Cited by
- 44 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsComplstatement · cited by 351
- Submodule.IsTopComplstatement and proof · cited by 89
Cited by47
Results whose statement or proof uses this declaration.
- Submodule.projectionOntoLproof · cited by 20
- Submodule.IsTopCompl.symmproof · cited by 14
- Submodule.quotientEquivOfIsTopComplproof · cited by 7
- Submodule.prodEquivOfIsTopComplproof · cited by 6
- Submodule.orthogonalProjectionOnto_norm_leproof · cited by 6
- Submodule.projectionOntoL_apply_leftproof · cited by 3
- Submodule.projectionL_add_projectionL_eq_selfproof · cited by 2
- Submodule.IsTopCompl.continuous_projectionstatement · cited by 2
- Submodule.ker_projectionOntoLproof · cited by 2
- Submodule.isIdempotentElem_projectionLproof · cited by 1
- ContinuousLinearMap.FredholmPackage.isQuasiInverseproof · cited by 1
- Submodule.IsTopCompl.continuous_projectionOntostatement and proof · cited by 1