Theorems · Theorem · functional analysis
ClosedSubmodule.toSubmodule_sSup
∀ {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] (S : Set (ClosedSubmodule R N)),
↑(sSup S) = ↑(⨆ s ∈ S, ↑s).closure- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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 · cited by 7,192
- iSupstatement · cited by 2,415
- SupSet.sSupstatement · cited by 954
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.toSubmodule_iSupproof · cited by 1