Theorems · Theorem · functional analysis
ContinuousMultilinearMap.map_coord_zero
∀ {R : Type u} {ι : Type v} {M₁ : ι → Type w₁} {M₂ : Type w₂} [inst : Semiring R]
[inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : AddCommMonoid M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
[inst_4 : Module R M₂] [inst_5 : (i : ι) → TopologicalSpace (M₁ i)] [inst_6 : TopologicalSpace M₂]
(f : ContinuousMultilinearMap R M₁ M₂) {m : (i : ι) → M₁ i} (i : ι), m i = 0 → f m = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- ContinuousMultilinearMap.toMultilinearMapproof · cited by 70
- MultilinearMap.map_coord_zeroproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- HasFPowerSeriesWithinOnBall.coeff_zeroproof · cited by 5
- ContinuousMultilinearMap.integral_applyproof · cited by 1
- HasFiniteFPowerSeriesAt.compproof · cited by 1
- FormalMultilinearSeries.comp_idproof · cited by 1