Theorems · Theorem · functional analysis
ClosedSubmodule.toSubmodule_iSup
∀ {ι : Sort u_1} {R : Type u_2} {N : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid N]
[inst_2 : TopologicalSpace N] [inst_3 : Module R N] [inst_4 : ContinuousAdd N] [inst_5 : ContinuousConstSMul R N]
(f : ι → ClosedSubmodule R N), ↑(⨆ i, f i) = ↑(⨆ i, ↑(f i)).closure- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement and proof · cited by 51
- iSup_rangeproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.coe_iSupproof · cited by 1