Theorems · Theorem · operator theory
IsCompactOperator.smul
∀ {M₁ : Type u_3} {M₂ : Type u_4} [inst : TopologicalSpace M₁] [inst_1 : AddCommMonoid M₁]
[inst_2 : TopologicalSpace M₂] [inst_3 : AddCommMonoid M₂] {S : Type u_6} [inst_4 : Monoid S]
[inst_5 : DistribMulAction S M₂] [ContinuousConstSMul S M₂] {f : M₁ → M₂},
IsCompactOperator f → ∀ (c : S), IsCompactOperator (c • f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Monoidstatement and proof · cited by 3,887
- IsCompactproof · cited by 1,282
- ContinuousConstSMulstatement and proof · cited by 832
- DistribMulActionstatement and proof · cited by 584
- Filter.mem_of_supersetproof · cited by 308
- continuous_idproof · cited by 192
- IsCompact.imageproof · cited by 105
Cited by1
Results whose statement or proof uses this declaration.
- IsCompactOperator.smul_unit_iffproof · cited by 1