Theorems · Theorem · general topology
BoundedContinuousFunction.coe_sum
∀ {α : Type u} {R : Type u_2} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace R] {ι : Type u_3} (s : Finset ι)
[inst_2 : AddCommMonoid R] [inst_3 : BoundedAdd R] [inst_4 : ContinuousAdd R] (f : ι → BoundedContinuousFunction α R),
⇑(∑ i ∈ s, f i) = ∑ i ∈ s, ⇑(f i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- PseudoMetricSpacestatement and proof · cited by 1,550
- ContinuousAddstatement and proof · cited by 777
- BoundedContinuousFunctionstatement and proof · cited by 511
- map_sumproof · cited by 455
- BoundedAddstatement and proof · cited by 18
- BoundedContinuousFunction.coeFnAddMonoidHomproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.charAlgHom_applyproof · cited by 3
- BoundedContinuousFunction.sum_applyproof · cited by 0