Theorems · Theorem · operator theory
IsCompactOperator.codRestrict
∀ {R₂ : Type u_1} [inst : Semiring R₂] {M₁ : Type u_2} {M₂ : Type u_3} [inst_1 : TopologicalSpace M₁]
[inst_2 : TopologicalSpace M₂] [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R₂ M₂]
{f : M₁ → M₂},
IsCompactOperator f →
∀ {V : Submodule R₂ M₂} (hV : ∀ (x : M₁), f x ∈ V), IsClosed ↑V → IsCompactOperator (Set.codRestrict f (↑V) hV)- 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.
Cites16
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
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.Elemstatement · cited by 7,166
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- IsClosedstatement and proof · cited by 1,639
- IsCompactproof · cited by 1,282
Cited by1
Results whose statement or proof uses this declaration.
- IsCompactOperator.restrictproof · cited by 1