Theorems · Theorem · functional analysis
Submodule.toLinearMap_projectionL
∀ {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} (h : Submodule.IsTopCompl p q), ↑(p.projectionL q h) = p.projection q ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- ContinuousLinearMap.toLinearMapstatement · cited by 528
- Submodule.IsTopComplstatement and proof · cited by 89
- Submodule.projectionstatement · cited by 63
- Submodule.IsTopCompl.isComplstatement · cited by 44
- Submodule.projectionLstatement · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.isStrictMap_isClosed_range_iff_quotientproof · cited by 0