Theorems · Theorem · functional analysis
Submodule.IsTopCompl.symm
∀ {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} [ContinuousSub M], Submodule.IsTopCompl p q → Submodule.IsTopCompl q p- Cited by
- 14 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Continuousproof · cited by 2,592
- continuous_idproof · cited by 192
- Submodule.IsTopComplstatement and proof · cited by 89
- IsCompl.symmproof · cited by 80
Cited by14
Results whose statement or proof uses this declaration.
- Submodule.IsTopCompl.isClosedproof · cited by 3
- Submodule.IsCompl.isTopCompl_of_finiteDimensional_quotientproof · cited by 3
- Submodule.IsCompl.isTopCompl_iff_continuous_symm_prodEquivOfIsComplproof · cited by 2
- Submodule.projectionL_add_projectionL_eq_selfstatement · cited by 2
- Submodule.projectionL_eq_self_sub_projectionLstatement and proof · cited by 1
- Submodule.isTopCompl_commproof · cited by 1
- Submodule.ClosedComplemented.of_disjoint_of_finiteDimensional_quotientproof · cited by 1
- Submodule.projectionL_eq_id_sub_projectionLstatement · cited by 0
- ContinuousLinearMap.closedComplemented_ker_of_rightInverseproof · cited by 0
- ContinuousLinearMap.isStrictMap_isClosed_range_iff_quotientproof · cited by 0
- Submodule.prodEquivOfIsTopCompl_symm_applystatement · cited by 0
- ContinuousLinearMap.ofIsTopCompl_eq_addstatement and proof · cited by 0