Theorems · Theorem · functional analysis
ContinuousMultilinearMap.mkPiRing_apply
∀ {R : Type u} {ι : Type v} {M : Type u_1} [inst : Fintype ι] [inst_1 : CommRing R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] [inst_4 : TopologicalSpace R] [inst_5 : TopologicalSpace M] [inst_6 : ContinuousMul R]
[inst_7 : ContinuousSMul R M] (z : M) (m : ι → R), (ContinuousMultilinearMap.mkPiRing R ι z) m = (∏ i, m i) • z- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement · cited by 3,473
- Finset.prodstatement · cited by 2,356
- ContinuousMultilinearMapstatement · cited by 1,016
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousMulstatement and proof · cited by 343
- ContinuousMultilinearMap.mkPiRingstatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.mkPiRing_zeroproof · cited by 1